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U.S. Highway Numbering

Are u.s. interstate highways numbered according to a pattern, david mikkelson, published nov 13, 2001.

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Most of us probably don't stop to ponder why the maze of U.S. interstates and highways we travel in our automobiles are numbered the way they are — just trying to find the correct road, get on it heading the right direction, and exit at the proper off-ramp is challenge enough. There actually is a rhyme and a reason to the numbering system used for U.S. highways, although the rhymes and reasons vary for different types of roads. Highways generally fall into one of three classes which generally use similar (but not identical) rules in assigning numbers:

Interstate highways established under the aegis of the Federal Aid Highway Act of 1956.

U.S. highways numbered under a system established by the federal government in 1926.

Regional roads numbered under individual state and county systems.

INTERSTATE HIGHWAYS:

Under the plan developed for a national interstate highway system during the Eisenhower administration, interstate highways (marked with the familiar red-and-blue shields) are numbered according to the following rules:

Major interstate highways are identified by one- or two-digit numbers. North-south routes are assigned odd numbers, with the numbers growing larger from west to east; east-west routes are assigned even numbers, with the numbers growing larger from south to north.

NORTH-SOUTH EXAMPLES: Interstate 5 runs through California, Oregon, and Washington, from the Mexican border to the Canadian border. Interstate 95 traverses the east coast from the Canadian border near Houlton, Maine, to Florida's southern tip in Miami. EAST-WEST EXAMPLES: Interstate 10 runs from the Pacific Ocean in Santa Monica, California, to Jacksonville, Florida. Interstate 90 crosses the USA from Seattle, Washington, to Boston, Massachusetts.

(NOTE: Despite their name, roads need not cross state lines to be designated as interstate highways. Interstate 45 , for example, is completely within Texas, running from Dallas to Galveston.)

Interstate routes that branch off major, long-distance routes are assigned three-digit numbers. The last two numbers indicate the parent route, and the first digit signifies the road's function (i.e., an odd digit for a spur running directly to a city; an even digit for a road that loops around a metropolitan area).

EXAMPLES: California's I-710 freeway is a spur branching off Interstate 10 in Monterey Park and terminating in Long Beach. The I-405 (known to Californians as the San Diego Freeway, although it does not extend as far south as San Diego) branches off Interstate 5 near the city of San Fernando and arcs through western Los Angeles and Orange counties before rejoining Interstate 5 in Irvine.

(NOTE: Three-digit interstate highway numbers are not unique. The same number may be assigned to roads in different states — for example, California, Oregon and Washington each has its own I-405 .)

And, just to make things even more confusing, there are quirky exceptions to these rules:

Interstate 99 was assigned a high two-digit number (through legislation), even though it is not a major highway (it runs for only 58 miles between Wolfsburg and Bald Eagle in Pennsylvania) and is farther west than other interstates with lower numbers.

U.S. HIGHWAYS:

U.S. Highways (or Routes), marked with black-and-white badge-shaped signs, are assigned one- to three-digit numbers. Like interstate highways, they designate north-south roads with odd numbers and east-west roads with even numbers, but the numbering scheme is inverted: the numbers of north-south routes grow larger from east to west, and the numbers of east-west routes grow larger from north to south.

NORTH-SOUTH EXAMPLES: US Highway 1 runs from Fort Kent, Maine, to Key West, Florida. US Highway 99 used to run from the Canadian border at Blaine, Washington, almost to the Mexican border at the city of Calexico, California. (Highway 99 has since been supplanted by Interstate 5 and is no longer designated as a U.S. Highway.) EAST-WEST EXAMPLES: US Highway 14 runs from Chicago, Illinois to Yellowstone National Park in Wyoming. US Highway 82 runs from Alamogordo, New Mexico, to Brunswick, Georgia.

STATE AND COUNTY ROUTES:

Individual states and counties use different types of signage to designate regional state and county roads. For the most part, states follow the Interstate and U.S. Highway patterns of assigning odd numbers to north-south routes and even numbers to east-west routes, but as always there are exceptions. California's Antelope Valley Freeway runs almost due north from the Los Angeles basin through the high desert, yet it's the 14 Freeway.

In answer to that perennial trivia question, the state of Hawaii has three roads designated as interstate highways (all of them on the island of Oahu) because roads established under the purview of the Federal Aid Highway Act and receiving funding from the federal government are considered interstate highways, even if they fall completely within the borders of a single state. Hawaii's interstate highways are somewhat different than other interstates in that they are identified with numbers preceded by the letter H< rather than the standard I, however.

Blocksma, Mary.   Reading the Numbers .     New York: Penguin Books, 1989   (pp. 96-99).

Richard.   "Highway Numerology Muddled by Potholes in Logic."     Los Angeles Times.   13 November 2001   (p. B2).

By David Mikkelson

David Mikkelson founded the site now known as snopes.com back in 1994.

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Here’s the Surprising Logic Behind America’s Interstate Highway Numbers

There’s a method to the madness—mostly.

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Next time you're cruising on the interstate, take some time to spot all the different highway shields. Are there single digits? Double? Triple, even? What do the odd and even numbers actually mean? Believe it or not, there's a legit method behind the madness that makes up the United States interstate highway system and how they get their numbers.

Way back in 1926, the U.S. Numbered Highway System was established, setting the groundwork for how the nation's highways would be named and labeled. But it was the Federal Aid Highway Act of 1956 that actually helped establish the interstate numbering system that we're talking about here today. To cite any federal standards would be boring and confusing to take in all at once; thankfully, we have YouTuber CGP Grey to walk us through this. Let's take a virtual trip across America to understand just how this all works.

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Just a quick note before you jump into the comments and yell at me: yes, there are exceptions, and I don't get paid nearly enough to make the rules of the nation's highways (I've asked, believe me). So don't shoot the messenger, just soak up the sweet, sweet knowledge.

First, let's talk major interstates. Essentially all of these highway systems have double-digit numbers, with just one pesky exception. East-west highway systems all end with "0" and are numbered increasingly higher as you progress further north. For example, I-10 runs through the southernmost states (California, Arizona, New Mexico, Texas, Louisiana, Mississippi, Alabama, and Florida), while I-90 makes its way across some of the northernmost (Washington, Idaho, Montana, South Dakota, Wisconsin, Illinois, Indiana, Ohio, Pennsylvania, New York, and Massachusetts).

North-south interstates end with a 5 and are numbered increasingly higher as you progress further east. For example, the westernmost major highway system running between California, Oregon, and Washington is I-5, and the easternmost is I-95, which travels through Florida, Georgia, South Carolina, North Carolina, Virginia, Maryland, Delaware, Pennsylvania, New Jersey, New York, Connecticut, Rhode Island, Massachusetts, New Hampshire, and Maine.

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There are also plenty of interstates that don't actually cross into other states. Texas has the only major interstate like this, and it follows the same naming convention as the rest of the continental U.S. Alaska, Hawaii, and Puerto Rico all have their own special naming convention that doesn't exactly follow the standard system we're talking about here, too.

Next up comes interstate mediums, which are suffixed with either an even or odd number. Evens mean that the interstate is east-west, and odds are north-south. Multiple medium interstates can exist with the same number. As the video below points out, I-76 is a highway in Colorado, and it's also the interstate number of the Pennsylvania Turnpike. There are plenty of other examples of this across the U.S. as well.

Then there are minor interstates, all of which are represented by three digits instead of the usual two. The first number in the three-digit sequence is the secret sauce, while the last two represent the major interstate that it branched from. If the first digit is even, the interstate will eventually branch back into its parent; these are called "bypasses," or "beltways" when encircling a landmark like a city. An interstate with an odd-numbered first digit is called a "spur" and will not connect back to its parent. If a minor interstate connects two major interstates, it is generally up to the state to decide which major interstate is used as the suffix of the minor.

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Now you know the secrets of the major interstates in the U.S., so if your GPS ever acts up and all of the maps suddenly vanished, at least you'll be able to navigate the highways across the States.

If you're more interested in knowing the exceptions to the norms, CGP Grey does a great job at showing them off. You can watch his video, complete with fun little stick-figure animations, below.

Got a tip or question for the author? You can reach them here: [email protected]

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Flight Numbers Explained: How Airlines Decide Route Numbers

Grant Martin

Sitting in a bright corner office of the ninth floor of Chicago's Willis Tower, Patrick Quayle, VP of international network at United Airlines, beams as I walk in to meet him. Earlier this month, United Airlines announced new service between Newark and Cape Town, South Africa, one of the first carriers in the United States to ever offer that route, and the airline's only service into sub-Saharan Africa.

We're here to talk not necessarily about why United chose that route, but how the route number was selected: fight 1122 from EWR-CPT and 1123 on the way back.

But let's back up for a minute: each flight operated in commercial airspace has a number associated with it, a label that easily tells planners (and knowledgeable passengers) where an airplane is headed, and between what two airports. In many cases, those flight numbers repeat daily; flight 100 on American Airlines always goes between JFK and London Heathrow seven days a week, while 101 runs the same route in reverse.

In some special cases, the routes have a special meaning. Boarding flight 1 to any destination is often a matter of prestige. Whether it's British Airways's flight BA1 from London to New York — once flown by the Concorde, now by the Airbus A318 in all-business configuration — or United's UA1 from San Francisco to Singapore, flight 1 is often a flight of distinction, operated with a flagship aircraft and special service.

But how do airlines decide what route gets labeled flight 1, or how any particular route gets numbered? The answer lies in a complex set of tiers combining traditional and modern rules, tweaked to each carrier specifically. And while no naming convention is identical between airlines, there are some parallel trends as well as some red-hot flight numbers that most airlines tend to avoid.

At United, that process starts and stops at Quayle's desk. Together with Ted Novkov, United's Director - Network Planning and International Scheduling, and a team of route network planners, Quayle helps pick flight numbers via a combination of manual and automatic tools to ensure that there are no repeat numbers and potential safety issues.

At American, there's a similar setup. I tracked down Brent Alex, American's Manager of Global Airport Access and Network Planning, to chat about the same topic and figure out what goes into naming AA1 versus AA100.

Overall Trends

There are definitely similarities in the ways that many carriers select route numbers. In general, lower flight numbers are assigned to international flights, though the merger of multiple carriers over the years has muddied many of the old delineations. At United, for example, flights 1 to 200 are assigned primarily to international routes from the Continental era, before the two carriers merged. 800-1000 are now United international routes. Google any flights in the low hundreds across American, Delta or United, though, and there's a high probability that that route will serve an international destination.

Where possible, adjacent numbers are often chosen for the same flight going in the opposite direction. DL6, for example, flies from Haneda, Japan to Los Angeles. Flight 7 is the same route in reverse.

There's also a bit of a trend in the way that flights are numbered by the direction in which the aircraft operates, though many of those old rules have also been diluted by mergers and growth, especially on the domestic front.

LAX Airport, March 2019 (Photo by Alberto Riva/TPG)

"From a domestic system (point of view), that's true," says Alex at American. "Internationally, our flights generally are even going east, odd going west. And then odd going south, even going north."

Brackets for a carrier's mainline versus regional fleet are also typically used. At American, flights 1 to 2949 are all assigned to the mainline fleet while 2950 to 6099 are all reserved for swaths of regional partners such as Skywest or Envoy. Delta and United use a similar formula. This helps route planners and other staff quickly identify which carrier is operating a flight and often where it's headed.

How Flight Numbers Are (And Are Not) Selected

So what happens when an airline launches a new route and a new flight number is needed?

At legacy carriers, a combination of manual and automatic tools are used to figure out what flight numbers are open within a specific bracket. American, specifically, uses a tool called FNOM, or the Flight Number Optimization Model, to automatically search for route numbers, consider the overall schedule and suggest possible numbers. "We use the automatic tool mostly for the domestic system where we don't have as much of a preference on what the numbers are," says Alex at American. "In that automated tool there is a function where those international numbers will kind of be locked down so they can only be assigned to that route."

Lest one think that the tool simply picks the lowest available number and assigns it to the route accordingly, there's much more nuance to the process. "[United's tool] looks at things like consistency and what's being published. If a certain number is already published, let's keep it the same. It's very smart in the sense that it doesn't create unnecessary schedule changes, and at the same time, we have our international flight numbers that we restrict, saying 'Don't use those because we have them for international'," says Novkov at United.

That careful balance between manual and automatic selection also keeps the airlines out of hot water when considering certain flight numbers across the network. At American and United specifically, flight numbers associated with the 9/11 terrorist attacks have been permanently retired. Flights that have crashed often have their number retired: Swissair eliminated SR111 after the 1988 accident when an MD-11 plunged into the Atlantic; Air France doesn't fly AF447 anymore, which crashed in 2009; and you won't find MH370 and MH17 — two flights that gained worldwide recognition for the wrong reasons — in the Malaysia Airlines timetable.

Route numbers to and from China are also often carefully picked. "The number eight is lucky for China," says Quayle at United. "If you'll notice, we have flight 88 which is New York to Beijing. We have flight 8 which is San Francisco to Chengdu. Because eight is a lucky number in China, we fly eights to China. But four is an unlucky number, so we make a point not to do that. "

Flight 666 is also generally avoided by air carriers unless its part of a marketing campaign like Finnair's flight 666 to Helsinki (HEL) a few years back.

Airlines can also organize flight numbers in blocks that indicate at a glance where they are going. For example, with typical German precision, Lufthansa divides the world by flight number: LH400 to LH499 are flights to North America, South America gets flights in the 500s, Africa from 560 to 599, the Middle East and Central Asia is the 600s, and Asia-Pacific the 700s. Even numbers are outbound from the home country, and odd numbers fly back. (British does it the other way; odd flights are outbound, starting from that BA1 to New York.) The geography-based model is in use at other airlines too: On Alitalia, for example, if your flight is in the 600s you know you're going to the Americas, and in the 700s to Asia.

As it turns out, United flight 1122 from Newark to Cape Town was chosen because that was the first date — November 22nd — that Quayle visited South Africa when he was a youngster. Meaningful to him and a handful of people in his network, of course, but most people flying across the Atlantic will never know the significance of that route number. Many more stories of how a particular route got its number may never get told.

This story has been amended with Patrick Quayle's correct title and name spelling.

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What's the Secret Behind the Numbers on the Interstate Signs?

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If you've ever driven west on Interstate 80 through Nebraska, you've seen one of the flattest and emptiest roads in America ... and you probably had some time to ponder life's most important questions. For example, why is the highway called "I-80," anyway? And why do some interstate names have one, two or three digits?

Buckle up, you're about to find out the secret codes behind the U.S. interstate naming system.

But for starters, let's find out how the Interstate Highway System began. The formal name for these roadways is The Dwight D. Eisenhower National System of Interstate and Defense Highways, and the project was approved by Congress through the Federal Aid Highway Act of 1956. It authorized the construction of about 41,000 miles (65,983 kilometers) of highways, stretching across the country from east to west and north to south.

One of the main purposes of the interstate system was national defense. President Eisenhower had served as the Supreme Commander of Allied Forces during World War II in Europe, and he'd witnessed the importance of Germany's Autobahn network , which allowed for speedy transportation throughout the country.

Another, more ominous selling point? The quick evacuation of cities that suffered potential atomic attacks .

And of course, the system was touted as a way for all Americans to travel with fewer traffic jams and more efficient routes. With no at-grade crossings (that is, intersections), the system used overpasses and underpasses to allow for seamless, stop-free, high-speed travel. There are now 46,876 miles (75,439 kilometers) of roadway with the interstate designation.

Construction began in 1956 in Missouri on what's now named I-70 , but the system as a whole wasn't completed until 1992 , when crews finished a devilishly difficult stretch in Glenwood Canyon, Colorado, where you'll find 40 bridges and viaducts on a single 12-mile (19-kilometer) stretch.

u.s. highway system in 1958

The Interstate Highway System transformed American life. The cargo trucking industry arose, gas stations and truck stops blossomed, suburbs sprung up around cities, and the concept of the "road trip" entered the national lexicon.

And as those road trippers zipped along, some of them surely wondered why interstates have various numbering systems. Why is one named I-5 while another is I-480? Let's take a closer look at the digits on those red, white, and blue shield-shaped signs.

Those Highway Numbers Aren't Random

The number of digits in the name tells you whether an interstate connects more than one city, or if it serves a single metropolitan area. Interstates with one or two digits (e.g., I-95) interconnect several regions. Those with three digits (e.g., I-285), on the other hand, are meant to serve a single city and are called auxiliary interstate highways. They connect to longer two-digit highways. The last two digits match the parent highway – for example, I-480 in Omaha is a 5-mile stretch that connects I-80 in Nebraska with I-29 in Iowa. Likewise, I-285 circles Atlanta and connects to I-85, going north and south.

Even-numbered interstates stretch east-west, while those with odd numbers move traffic north-south. Numbering for east-west highways starts in the south and moves north, so I-10 anchors the bottom border (Santa Monica, California, to Jacksonville, Florida), and I-90 is near the country's northern border (Seattle to Boston).

For north-south interstates, numbering begins in the west, starting with I-5, parallel to the West Coast. The easternmost interstate is I-95, running on the East Coast, from Houlton, Maine, to Miami.

There are some rare exceptions to this pattern, in cases where stretches of road were added after the first framework was already in place. For example, I-99 didn't receive its interstate designation until 1998, and it lies west of I-95 in eastern Pennsylvania.

Just two interstates split as they move through major cities. One is I-35E and I-35W in Minneapolis-St. Paul metro area; the other is I-35E and I-35W, which move through Dallas and Fort Worth, respectively.

The first digit of a three-digit interstate tips you off to its purpose. Connectors or spurs that only intersect one time mostly receive odd-numbered first digits. Even-numbered first digits, however, tend to be bypasses and loops that intersect with their parent interstate in two locations.

The names of major interstates are never repeated; they are always unique. However, some lesser stretches use the same two-digit numbers. For example, both New York and North Carolina have an I-87. There are also I-76s in both Colorado and Pennsylvania.

Three-digit interstates, however, can be used as often as necessary throughout the country, but they can't be repeated within a single state.

The Numerical Interstate System Can Get Messy

For instance, in San Francisco there's I-238, even though there's no I-38 for it to connect to – instead, it's an artery between I-880 and I-580. But because California already had so many roads, the appropriate digits were already in use with other roadways.

There are other exceptions, too. Alaska, Hawaii and Puerto Rico all have interstates, even though these roads don't connect to other states. They have special lettered designations: Alaska has A1 through A4 , Hawaii has an H1 through H3 and Puerto Rico has a PR1 and PR2 .

State highway naming convention differs a bit from the interstates. These roadways, which are denoted by black-and-white signs with badge symbols, use the same system of odd numbers for north-south routes, and even numbers for east-west routes. However, the number system is flip-flopped. The numbers on east-west roads get larger as you go from north to south, and the numbers on north-south highways increase as you go from east to west across the state.

I-90 is the longest U.S. interstate , stretching all the way from Boston to Seattle and covering nearly 3,100 miles (5,000 kilometers). It traverses 13 states. I-95, which connects Miami to Houlton, Maine, cuts through the most states of all the interstates – 15, and it also goes through Washington, D.C.

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The United States has a complex national highway system that is roughly 160,000 miles long. For foreign visitors wishing to drive around, it is helpful to understand how the roads are named and numbered. You never know when this knowledge will come in handy.

U.S. Interstate Map

Major Interstate Freeways

U.S. Interstate I-5

All major freeways that span across several states have one or two-digit numbers. Odd number means the freeway runs north-south, while even numbered freeways travel east and west. For example, interstate 5 (I-5) goes all the way from the Southern border in San Diego to the Northern border in Blaine, WA. I-10, on the other hand, connects the West Coast of San Diego and the East Coast of Jacksonville, FL.

Odd freeway numbers start from the West Coast, and increase toward east. I-5 is the first major north/South freeway, and it sits right by the Pacific Ocean. The next one is I-15, then I-25, and all the way to I-95 which is located along the East Coast.

Even freeway numbers start from south, and increase toward north. I-10 is the first interstate along the Southern border. Above I-10 is I-20, then I-30, and up until I-90.

Three-Digit Interstate Freeways

Three-digit highways connect to other major interstates. For example, 405 is a highway that is connected to I-5, while 215 is off I-15.

If the first digit is an odd number, the highway is likely to have only one end connected to a major highway. For example, 710 is a "spur" route that leaves I-10 and goes into the city of Long Beach.

If the first digit is an even number, the highway is usually connected to a major interstate at both ends. 405 splits from I-5 at one end (Lake Forest), but rejoins I-5 at the other end just north of Los Angeles. So they are often referred to as loops or "beltways."

U.S. Routes

Other than the Interstate Highway System mentioned above, there is also a grid of U.S. highways, more often referred to as U.S. routes.

Major U.S. routes are two-digit numbers. North-south routes are odd-numbered, and east-west even-numbered. However, what is different from the Interstate Highway System is that lowest odd numbers are in the east and highest numbers in the west. Similarly, the lowest even numbers are in the north and increase toward the south. For example, U.S. Route 1 runs north-south on the east coast, while Route 101 is located in California. Note that 101 is actually considered a two-digit highway.

Three-digit U.S. routes are "spur" highways, but unlike the interstate system, they may or may not have direct connection to their parent routes.

In general, U.S. routes are older roads and have largely been replaced by the newer and more functional Interstate Highway System. However, the grid of U.S. routes is still a major part of the country's transportation network, used by many local residents or as scenic drives.

Highway Mile Markers

You may have noticed those mile markers along interstates. They can help you estimate how far you have traveled into a state and how far away you are from your destination.

Mile markers always start at the state line in the south (for north-south highways), or in the west (for east-west highways). So if you enter Oregon from California, you will see mile 1 soon after you cross the state line, and then see increasing numbers as you travel north.

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odd numbers travel

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Numbering the Highway System

odd numbers travel

Knowing your numbers helps you know which direction you are going on U.S. highways. Here's how the highway systems are numbered.

Interstate Highways

  • The interstate system totals 46,300 miles. All interstate highways are marked by blue signs with red tops.
  • The north-south highways have odd numbers with 1 or 2 digits, usually including a 5. The lowest numbers are on the West Coast and increase as they move east. For example, I-5 is on the West Coast, I-95 on the East Coast.
  • The east-west highways have even numbers with 1 or 2 digits. The lowest numbers are in the South and increase as they go north. For example, I-4 runs through Florida; I-96 is the northernmost route.
  • An interstate highway with 3 digits is a connector or offshoot of a main route.

U.S. Routes

  • U.S. routes are posted in black letters on white signs.
  • The north-south routes have odd numbers, with 1 to 3 digits. These numbers increase from east to west (just the opposite of the interstate system). For example, U.S. 1 runs along the East Coast; U.S. 101 runs along the West Coast.
  • The east-west routes have even numbers, with 1 to 3 digits. The lowest numbers are in the North and increase moving south (just the opposite of the interstates). For example, U.S. 2 runs along the Canadian border; U.S. 90 runs through Texas.

For the distance between many U.S. cities, see Road Mileages Between U.S. Cities at Infoplease.com.

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Specialty Dining Reservations for multiple rooms

By tolg , January 4, 2023 in Norwegian Cruise Line

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Cool Cruiser

My family of 5 is booked in two rooms as 2 separate accounts (not really sure why that is, perhaps because we booked through Costco??) How do we go about making reservations for specialty dining for all 5 of us? Does anyone have experience with this?

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Two Wheels Only

Just have 1 person make the reservation for everyone. NCL doesn't care who the people are and the reservation can be for more than the number of people in the stateroom. You could make a reservation for 6 and it could be you and 5 strangers.

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KeithJenner

You are likely to have to make reservations for 6, as there aren’t many slots released for odd numbers. There is no issue with a group of 5 booking a table for 6.

kayjay76

3 hours ago, tolg said: My family of 5 is booked in two rooms as 2 separate accounts (not really sure why that is, perhaps because we booked through Costco??) How do we go about making reservations for specialty dining for all 5 of us? Does anyone have experience with this?

like the others said... make the reservation for 5 or 6 people. when you get there or are finished eating (can't remeber which) they will take your cards and deduct a dinner if you have free 2 dining or charge the guests room. the whole process is super simple 

5 hours ago, KeithJenner said: as there aren’t many slots released for odd numbers

There aren't ANY slots for odd numbers.  All the tables have an even number of seats.  Anyone with an odd number of people should book a table for one person more than they have so as to ensure they get the proper table size reserved.

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15 minutes ago, hallux said: There aren't ANY slots for odd numbers.  All the tables have an even number of seats.  Anyone with an odd number of people should book a table for one person more than they have so as to ensure they get the proper table size reserved.

You do see reservations available for odd numbers at times.

We used to travel as a group of three and I have made reservations for three a few times, but more often than not we had to go for four.

It is possible that they have stopped offering them recently, but you certainly used to be able to get the occasional table for odd numbers pre covid.

  • 2 weeks later...

farmecologist

On 1/4/2023 at 7:19 AM, KeithJenner said: You do see reservations available for odd numbers at times.   We used to travel as a group of three and I have made reservations for three a few times, but more often than not we had to go for four.   It is possible that they have stopped offering them recently, but you certainly used to be able to get the occasional table for odd numbers pre covid.  

Thanks for the info!  In our situation we have a party of 2...and no more reservation slots exist for only 2 people ( at Ocean Blue ).  However, reservations for 4 people do exist.  Will there be ramifications if I book the 4 person table but only the two of us show up?  BTW - NCL will let me do this...but just wondering if there are unspecified ramifications, etc...

55 minutes ago, farmecologist said:   Thanks for the info!  In our situation we have a party of 2...and no more reservation slots exist for only 2 people ( at Ocean Blue ).  However, reservations for 4 people do exist.  Will there be ramifications if I book the 4 person table but only the two of us show up?  BTW - NCL will let me do this...but just wondering if there are unspecified ramifications, etc...   Thanks!        

I’ve never done this, but If I booked a table for 4 when there were only two of us then I would certainly get it adjusted onboard.

I doubt whether two of you turning up would cause you a major problem, but you would be using a table that could have been used by a group of 4.   

But this is all speculation from my point, as I’ve never done what you describe. Three people will be seated at a table for four, so for us it doesn’t make as much difference as it would for a couple.

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BirdTravels

1 hour ago, farmecologist said:   Thanks for the info!  In our situation we have a party of 2...and no more reservation slots exist for only 2 people ( at Ocean Blue ).  However, reservations for 4 people do exist.  Will there be ramifications if I book the 4 person table but only the two of us show up?  BTW - NCL will let me do this...but just wondering if there are unspecified ramifications, etc...

So,,, bookings open 120 prior to departure (130 for Haven, 125 for Club Balcony and Top Tier Latitudes). You should book exactly 120 days prior to departure for the best restaurant selection.  If you are only seeing 4-tops, that means that you waited to long and other reservations are sold out. 

Technically , there is no problem with booking a 4-top.

BUT,,, you are taking a table that a group of 4 may need. Keep your 4-top. Change as soon as you embark to 2 so that groups of 3 and 4 can get a table at the restaurant. 

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Odd Numbers – Definition with Examples

What are odd numbers, how to identify odd numbers, types of odd numbers, solved examples of odd numbers, practice problems of odd numbers, frequently asked questions of odd numbers.

A number which is not divisible by “2” is called an odd number. An odd number always ends in 1, 3, 5, 7, or 9 .

Examples of odd numbers: $51,\;-\; 543, 8765,\;-\; 97, 9$, etc.

An odd number is always 1 more than (or 1 less than ) an even number. For example, let us take an even number, 8. The odd number next to it is $8 + 1 = 9$. The odd number before it is $8 \;-\; 1 = 7$.

This explains that when you have an odd number of objects with you, you cannot divide them into equal groups !

Odd number of pens

Odd numbers are numbers which when divided by 2 leave the remainder 1. 

In other words, we can say a number, which is not divisible by 2, is an odd number.

Examples: 1, 23, 535, 67, 12763489

Definition of Odd Numbers

Odd number can be defined as an integer that is not divisible by “2.” 

These are the numbers that have 1, 3, 5, 7, or 9 at their ones place . Odd numbers are simply the integers that are not multiples of 2.

Related Games

10 and 100 More than the Same Number Game

Let’s see how we identify odd numbers. Always look at the ones digit. If it is 1, 3, 5, 7, or 9, the number is odd. Otherwise, it is an even number.

Identifying odd numbers

Related Worksheets

10 and 100 More than a 3-digit Number

List of Odd Numbers $(1\;–\;200)$

The list of odd numbers from 1 to 200 is shown below. These are odd positive integers!

List of odd numbers from 1 to 200

There are two types of odd numbers given below:

Composite odd numbers:

The positive integers that have a factor other than 1 and itself are known as composite numbers. The numbers that are composite in nature but are not divisible by 2 are known as composite odd numbers. Example: 9, 15, 21          

Consecutive odd numbers:

If x is an odd number, then the numbers x and $\text{x} + 2$ are consecutive odd numbers. These numbers follow each other in sequential order with a difference of two between them.

Properties of Odd Numbers

Properties of addition.

  • Even number $+$ Odd number $=$ Odd number.

For example, $7 + 2 = 9$.

Even plus odd equals odd!

  • Odd number $+$ Odd number $=$ Even number.

For example, $5 + 9 = 14$

Odd plus odd equals even!

  • Even number $+$ Even number $=$ Even number

For example, $6 + 4 = 10$

Even plus even equals even!

Properties of Subtraction

  • Even number $-$ Odd number $=$ Odd number

For example, $10 \;-\; 5 = 5$.

  • Odd number $-$ Odd number $=$ Even number

For example, $11 \;-\; 3 = 8$.

Properties of Multiplication

  • Multiplying an even number and an odd number (and vice- versa) always results in an even number.

For example, $7 \times 4 = 28$.

  • Multiplying an even number with an even number always results in an even number.

For example, $2 \times 4 = 8$.

  • Multiplying an odd number with an odd number always results in an odd number.

For example, $7 \times 3 = 21$.

  • When we divide two odd numbers where the denominator is a factor of the numerator, the result is always  an odd number.

Example: When we divide 9 by 3 where 3 is a factor of 9, we get 3, which is an odd number.

When we divide two odd numbers and the denominator is not a factor of the numerator then the result is a decimal number.

Let’s Summarize!

Odd Numbers – Definition with Examples

Odd Numbers Between 1 to 20

Odd numbers between 1 to 20 which are the first ten odd numbers are as follows.

First ten odd numbers

What is the Smallest Odd Composite Number?

The smallest odd composite number is 9 .

Check the list of odd numbers: 1, 3, 5, 7, 9, 11, …

Among these, 1 is neither prime nor composite. The numbers 3, 5, and 7 are not composite numbers. That makes 9 the smallest composite number.

Numbers that have factors other than 1 and itself are composite numbers. For example, 15. 

15 is divisible by 1, 3, 6 and 15.

General Form of Odd Numbers

The general form of odd numbers is given by $2\text{k} + 1$, where $\text{k} \in \text{Z}$ (set of integers).

Fun Facts of Odd Numbers!

  • When you add all the odd numbers from 1 to any number, the sum that you get will always be a perfect square .
  • Example: The sum of odd numbers from 1 to 10 is 25, which is a perfect square.
  • 0 is an even number.
  • The first positive odd number is 1.
  • Odd numbers are sometimes referred to as “uneven numbers” (meaning “ not even ”). However, the term ‘odd numbers’ is commonly preferred. 

Let’s Sing!

One, three, five, seven and nine,

All standing in a straight line.

Divide them into equal teams,

One is left, and alone it seems!

Let’s Do This!

This is a fun activity. Put an odd number of beads in a box. Ask your child to count and determine if the total number of beads is even or odd. Next, give your child two empty boxes. Instruct them to divide the beads into the two boxes, such that each of them have an equal number of beads. Ask how many are left. Further, ask your child to pick out an even number of beads and then an odd number of beads. Show that the sum or difference of an even and odd number is odd. 

In this article we learned about odd numbers. We discussed a few odd numbers and saw a chart of odd numbers. We also learned their properties and rules. There are various multiplicity rules and properties of odd numbers, which solve various mathematical problems.

1. Identify odd numbers from the given list.

23, 46, 81, 73, 11, 8, 62

Solution: 

Odd numbers are 23, 81, 73, 11 because they are not divisible by 2.                                

2. Find the sum of odd numbers between 50 and 60.

The odd numbers that lies between 50 and 60 are

51, 53, 55, 57, 59

Sum of these numbers $= 51 + 53 + 55 + 57 + 59 = 275$

3. Check whether the sum of two odd numbers is odd or even.

We know  that an odd number is always 1 more than an even number. Let $2\text{x}$ and 2y be an even number. 

So, $2\text{x} + 1$ and $2\text{y} + 1$ be the odd numbers 

The sum of the numbers 

$= (2x + 1) + (2 y+ 1)$

$= 2 x + 2 y + 2$

$= 2(x + y + 1)$

Let $\text{X} = x + y + 1$

Therefore, $(2 x + 1) + (2 y+ 1) = 2\text{X} =$ Multiple of $2 =$ Even number

4.  What is the sum of the smallest and the largest 3-digit odd numbers?

Solution:  

The smallest 3-digit odd number $= 101$

The largest 3-digit odd number  $= 999$

Sum of the numbers $= 101 + 999 = 1100$

5. The lengths of the sides of a triangle are consecutive odd numbers. Then find out what the length of the longest side is if the perimeter of the triangle is 56 units?

Let y be a positive odd number, so the odd number next to y is, $y + 2$ and $y + 4$.

So, $y, y + 2, y + 4$ are the lengths of the triangle.

Since we know that the perimeter of triangle $=$ sum of all the sides

$\Rightarrow 56 = y + y + 2 + y + 4$

$\Rightarrow 56 = 3y + 6$

$\Rightarrow y = \frac{50}{6}$

$\Rightarrow y = 16.66$

Odd Numbers – Definition with Examples

Attend this quiz & Test your knowledge.

Find the three consecutive odd integer numbers whose sum is 123?

0 is an____ number., what is the smallest positive odd number, find the number from below which is not an odd number , find the group which has only odd numbers .

What is divisibility?

The capacity of a number to be evenly divided by any number, without leaving a remainder is said to be “divisible” and this property is called divisibility.

Is 1 an odd number?

Yes, 1 is an odd number because it is not divisible by 2.

Find the odd number that comes after 999?

The odd number after 999 is 1001.

What is the general form of an odd number?

Yes, to express an odd number we use a formula that is expressed as $2n \pm 1$, where, n $\in$ W.

Can odd numbers be negative?

Yes, integers that are not multiples of 2 are odd numbers. Thus, odd numbers can be positive or negative.

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Table of Contents

Last modified on August 3rd, 2023

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Odd numbers.

Odd numbers or integers are part of whole numbers that are partially divisible into pairs. Thus all numbers except the multiples of 2 are odd numbers. They are in the form of 2k+1, where k ∈ Z (integers) are called odd numbers.

Some examples are 1, 3, 5, 7, and so on. They are just the opposite of even numbers. Odd numbers can be represented on a number line:

odd numbers travel

Looking at the examples, we can consider whether all odd numbers are prime.

No, it is not. However, all prime numbers are odd except 2.

List of Odd Numbers

Practice writing the odd numbers from 1 to 1000.

Odd Numbers from 1 to 100

odd numbers travel

Odd Numbers from 101 to 200

Odd numbers from 201 to 300, odd numbers from 301 to 400, odd numbers from 401 to 500.

The 4 main properties are:

Adding 2 Odd Numbers

Any 2 odd numbers, when added, always gives an even number.

Odd number + Odd number = Even number

Let a and b are 2 odd numbers

They are written in the form

a = 2k 1  + 1, b = 2k 2  + 1 where k 1 , k 2  ∈ Z

Adding a and b, we get

(2k 1  + 1) + (2k 2  + 1)

=> 2k 1  + 2k 2  + 2

=> 2(k 1  + k 2  + 1)

This expression is divisible by 2s

Similarly, the sum of the first n odd numbers follow S n = n 2 rule.

Subtracting 2 Odd Numbers

When an odd number is subtracted from the other, it always gives an even number. It is similar to adding two odd numbers.

Odd Number – Odd number = Even number

Multiplication of 2 Odd Numbers

When an odd number is multiplied by another odd number, the product is also an odd number.

Odd number × Odd number = Odd number

Now, a × b = (2k 1  + 1)(2k 2  + 1)

=>4k 1  k 2  + 2k 1  + 2k 2  + 1

=>2(2k 1  k 2  + k 1  + k 2 ) + 1

This expression is an odd number

Division of 2 Odd Numbers

Division of 2 odd numbers always results in an odd number when the denominator is a factor of the numerator.

Odd number ÷ Odd number = Odd number

There are 2 types of odd numbers. They are:

Consecutive Odd Numbers

They are 2 odd numbers that come one after the other in a sequence. If ‘a’ is an odd number, then the consecutive odd number corresponding to a is ‘a + 2’.They can be positive or negative.

Positive Consecutive Odd Number

  • 101 and 103

Negative Consecutive Odd Number

  • -11 and -13
  • -51 and -53

Composite Odd Number

They are positive odd numbers obtained by multiplying 2 smaller positive integers or multiplying the number with 1.

Given are the composite odd numbers till 100:

9, 15, 21, 25, 27, 33, 35, 39, 45, 49, 51, 55, 57, 63, 65, 69, 75, 77, 81, 85, 87, 91, 93, 95, and 99.

Thus, the smallest odd composite number is 9.

Solved Examples

Determine if 145 is an odd number or not.

The given number is 145 Checking the divisibility of the number by 2, we get the remainder by 1, which proves that 145 is an odd number.

Simplify: a) (-5) + (-9) b) (-11) – (-3) c) (-3) × (-7) d) (-9) ÷ (-3)

a) (-5) + (-9) = -14 b)(-11) – (-3) = -8 c) (-3) × (-7) = 21 d) (-9) ÷ (-3) = 3

The sum of three consecutive odd numbers is 51. Find the numbers.

Let x be an odd number Then the next consecutive odd number are x + 2 and the next term is x + 2 + 2 = x + 4 Now, x + (x + 2) + (x + 4) = 3x + 6 = 51 => 3x = 51 – 6 => x = ${\dfrac{45}{3}}$ = 15 Hence, the other numbers are 15 + 2 = 17, 15 + 4 = 19 Thus the 3 consecutive odd numbers are 15, 17, and 19.

The sum of 5 consecutive odd numbers is 145. Find the third number in the sequence.

Let x be an odd number Then the next consecutive odd numbers are: x + 2 x + 2 + 2 = x + 4 x + 2 + 2 + 2 = x + 6 x + 2 + 2 + 2 + 2 = x + 8 Now, x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 5x + 20 = 145 => 5x = 145 – 20 => 5x = 125 => x = ${\dfrac{125}{5}}$ = 25 Hence, the other numbers are 25 + 2 = 27 27 + 2 = 29 29 + 2 = 31 31 + 2 = 33 Thus, the third number in the sequence is 29.

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Odd Numbers

Odd numbers are numbers that cannot be arranged in pairs. In other words, all numbers except the multiples of 2 are odd numbers. Let us learn more about odd numbers, the definition of odd numbers, the odd numbers list and some examples of odd numbers in this article.

What are Odd Numbers?

Odd numbers are those numbers that cannot be divided into two parts equally. In other words, odd numbers are positive integers that cannot be categorized into groups of two.

Meaning of Odd Numbers

Let us understand the meaning of odd numbers with the help of an example. If we observe numbers like, 1, 3, 5, 7, and so on, we see that these numbers cannot be paired. Let us visualize it using an example of shoes and cherries. Observe the figure given below in order to understand how the pairing of these numbers works. We have sets of shoes in counts of 1, 3, 5, and 7. On the other hand, we have cherries in pairs of 2, 4, 6, and 8.

odd numbers

It is to be noted here that the shoes, which show odd numbers, do not form complete pairs. One shoe among all remains unpaired. On the contrary, cherries that show even numbers are those numbers that can be divided into two parts equally and so they form complete pairs. For example, 4 cherries can be divided into 2 pairs of 2, 8 cherries can be divided into 4 pairs of 2, and so on.

Therefore, we can understand that odd numbers cannot be paired.

List of Odd Numbers

Let us have a look at the list of all the odd numbers from 1 to 200 and try to apply the knowledge we have learned here so far. Note that none of the numbers given here are multiples of 2. It should also be noted that out of the first 200 numbers, only 100 numbers are odd numbers. Have a look at the list of the odd numbers from 1 to 200 given here.

The definition that we have learned above is applied in this table and it eases our work, doesn't it? Observe the given table and try to notice some similarities between all these numbers given above.

  • Did you notice a pattern in the above odd numbers list?
  • In the odd numbers list, the digit at the ones place always remains 1, 3, 5, 7, or 9.

Properties of Odd Numbers

The following points list the properties of odd numbers. Each of these properties can be explained in a detailed way as given below.

  • Addition of Odd Numbers : The addition of two odd numbers always gives an even number, i.e., the sum of two odd numbers is always an even number. For example, 3 (odd) + 5 (odd) = 8 (even).
  • Subtraction of Odd Numbers : Subtraction of two odd numbers always results in an even number. For example, 7 (odd) - 1 (odd) = 6 (even).
  • Multiplication of Odd Numbers : Multiplication of two odd numbers always gives an odd number. For example, 3 (odd) × 7 (odd) = 21 (odd).
  • Division Of Odd Numbers : Division of two odd numbers always gives an odd number. For example, 33 (odd) ÷ 11 (odd) = 3 (odd).

Let us summarize these properties of odd numbers using the table given below.

Types of Odd Numbers

Odd numbers are a list of all the numbers that are not the multiples of 2. So this seems like a vast set of numbers. So we can have many types of odd numbers starting from whether the odd numbers have factors or not, what is the difference between two odd numbers, what is their position on the number line , etc.

Consecutive Odd Numbers

Consecutive odd numbers are those odd numbers that are listed in sequence of their order. For example, if n is an odd number, then the numbers n and n + 2 are grouped under the category of consecutive odd numbers. They always have a difference of 2 between them and are consecutive in nature, hence the name consecutive odd numbers. For example 3 and 5, 11 and 13, 25 and 27, 37 and 39, 49 and 51, and so on.

Composite Odd Numbers

Composite odd numbers are those odd numbers that are not prime numbers . These types of odd numbers are formed by the product of two smaller positive odd integers. The composite odd numbers from 1 to 100 are 9, 15, 21, 25, 27, 33, 35, 39, 45, 49, 51, 55, 57, 63, 65, 69, 75, 77, 81, 85, 87, 91, 93, 95, and 99.

Smallest Odd Number

The smallest odd number is 1 because odd numbers start from 1 and are listed as, 1, 3, 5, 7, 9, 11 and so on.

First 10 Odd Numbers

The first ten odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19.

Smallest Odd Composite Number

The smallest odd composite number is 9. If we start looking at the smallest composite number it is 4, but that is an even number. The next composite number is 6 which is again an even number. The same goes for the next composite number which is 8. Now, the next composite number is 9 which is an odd number. So, this brings us to the smallest odd composite number which is 9.

Odd Prime Numbers

Odd prime numbers means those prime numbers which are odd numbers. Interestingly, all prime numbers except 2 are odd numbers.

Odd Natural Numbers

Odd natural numbers mean natural numbers that are odd numbers. We know that natural numbers are positive counting numbers that start from 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and go on till infinity. Among these if we select the odd numbers, we get 1, 3, 5, 7, 9, and so on.

Tips and Tricks on Odd Numbers

Given below is a list of a few tips and tricks on odd numbers. These will help you in remembering the concepts faster.

  • The sum of two odd numbers is always an even number.
  • An easy method to differentiate whether a number is odd or even is to divide it by 2.
  • If the number is not divisible by 2 completely, it will leave a remainder of 1, which indicates that the number is an odd number and cannot be divided into 2 parts evenly.
  • If the number is divisible by 2 completely, it will leave a remainder 0, which indicates that it is an even number and it can be divided into 2 parts evenly.
  • Odd numbers always have 1, 3, 5, 7, or 9 in their units place. Even numbers always have 0, 2, 4, 6, or 8 in their units place.
  • Even Numbers
  • Real Numbers
  • Natural Numbers
  • Whole Numbers
  • Rational Numbers
  • Irrational Numbers
  • Counting Numbers
  • Cardinal Numbers
  • Odd Numbers 1 to 1000
  • Sum of Odd Numbers
  • Even and Odd Numbers Worksheets

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Examples of Odd Numbers

Example 1: Determine whether 135 is an odd number or not.

We can find this out using any of the given two methods:

Method 1: Check the digit on the units place. The units place of the number is 5, which is an odd number. This shows that the given number is an odd number. Therefore, 135 is an odd number.

Method 2: We need to check the divisibility of the number by 2. On dividing the given number 135 by 2, we get the remainder as 1. This proves that 135 is an odd number.

Therefore, we know that the number 135 is an odd number.

Example 2: Answer the following questions with reference to odd numbers:

a.) 1 is odd or even?

b.) Which is the smallest 4 digit odd number?

c.) What is the smallest odd composite number?

d.) What is the sum of any two odd numbers?

e.) Is 2 an odd number?

a.) 1 is an odd number.

b.) The smallest 4 digit odd number is 1001.

c.) The smallest odd composite number is 9.

d.) The sum of any two odd numbers is always an even number.

e.) No, 2 is not an odd number, it is an even number.

Example 3 : State true or false with respect to odd numbers.

a.) The sum of two odd numbers is always an even number.

b.) The smallest odd number is 5.

c.) All prime numbers are odd numbers.

d.) 9 is an odd number.

a.) True, the sum of two odd numbers is always an even number.

b.) False, the smallest odd number is 1.

c.) False, all prime numbers are not odd numbers, because 2 is a prime number which is even. It can be said that except 2, all prime numbers are odd.

d.) True, 9 is an odd number.

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Practice Questions on Odd Numbers

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FAQs on Odd Numbers

What are odd numbers in math.

In math, odd numbers are those numbers that are not the multiples of 2 . For example, 3, 5, 7, 9, and so on. Odd numbers cannot be arranged in pairs which means that they cannot be divided into two parts equally.

What are the Odd Numbers From 1 to 100?

The list of odd numbers from 1 to 100 is: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99.

What is the Difference Between an Odd Number and an Even Number?

The numbers which can be divided into two parts evenly are called even numbers. For example, 4, 8, 82, and so on are even numbers. Whereas odd numbers cannot be divided into equal pairs and are not divisible by 2. For example, 7, 91, 63, and so on are odd numbers.

What are Consecutive Odd Numbers?

Two consecutive odd numbers are those numbers that are odd and have a difference of 2 between them. For example 3 and 5, 11 and 13, and so on.

Is 0 an Even or Odd Number?

0 is an even number because it is attached with the multiples of 2. For example, 10, 20, 30 40, and so on. Therefore, it is not an odd number.

What is the Mean of the First Five Odd Numbers?

In order to find the mean of the first five odd numbers we need to follow the steps listed below:

  • Step 1: List the first five odd numbers, they are 1, 3, 5, 7, and 9.
  • Step 2: Calculate the sum → 1 + 3 + 5 + 7 + 9 = 25.
  • Step 3: Apply the mean formula = Mean of any n numbers = (Sum of n numbers) ÷ n = 25/5 = 5.

Therefore, the mean of the first five odd numbers is 5.

How Many Odd Numbers are there Between 36 and 53?

The list of odd numbers that lie between 36 and 53 are 37, 39, 41, 43, 45, 47, 49, and 51. Hence, there are a total of 8 odd numbers between 36 and 53.

Is Number 1 Odd or Even?

1 is an odd number because odd numbers are not divisible by 2 completely. For example, 3, 5, and 7 are a few odd numbers that cannot be divided equally into groups of 2..

Which Odd Number Comes After 499?

The odd number that comes after 499 is 501. The number that comes after 499 is 500 which is an even number. So, 501 is the next odd number after 499.

What is the Odd Numbers Formula?

The odd numbers formula is expressed as 2n ± 1, where, n ∈ W (whole numbers). We know that an odd number is always expressed as 1 less or more than an even number. An even number is expressed as 2n, where n is a whole number. Therefore, the formula for odd numbers is expressed as, Formula for odd numbers = 2n ± 1

What is the HCF of Two Consecutive Odd Numbers?

The Highest Common Factor (HCF) of any two consecutive odd numbers is always 1. For example, the HCF of 13 and 15 is 1.

What are Even and Odd Numbers?

All whole numbers can be categorized into two parts: even and odd numbers . Even numbers are the ones whose units place digit is either 0, 2, 4, 6, or 8, and odd numbers are ones whose units place digit is either 1, 3, 5, 7, or 9. Examples of even numbers are 2, 4, 6, 8, 10, 12, 14, 16, etc, and the examples of odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, etc.

What is the Smallest Odd Number and the First Odd Number?

1 is the smallest odd number because the list of odd numbers starts from 1, 3, 5, 7 and so on. So, 1 is the smallest and the first odd number.

What are 3 Consecutive Odd Integers?

3 consecutive odd integers are those numbers that are odd and have a difference of 2 between them. For example 3 and 5, 11 and 13, and so on.

  • Math Article

Odd Numbers

Odd numbers are the numbers that cannot be divided by 2 evenly. It cannot be divided into two separate integers evenly. If we divide an odd number by 2, then it will leave a remainder. The examples of odd numbers are 1, 3, 5, 7, etc.  Odd numbers are just the opposite concept of even numbers .  

The most simple way to remember an odd number is ‘it is not a multiple of 2’.  Here, all the concepts related to it like definition, examples, properties, types, etc. are covered. The key concepts that are covered here include the following.

What are Odd Numbers?

Odd numbers are defined as any number which cannot be divided by two. In other words, numbers in the form of 2k+1, where k ∈ Z (i.e. integers) are called odd numbers . It should be noted that numbers or sets of integers on a number line can either be odd or even.

Odd Numbers and Even Numbers

The numbers that are not odd, are even numbers, which are divisible by 2. Odd numbers cannot be divided into two parts equally but even numbers can be divided equally. For example, 4 can be divided and paired into two parts as 2-2, but 3 cannot be divided and paired.

Learn more:  Even And Odd Numbers

Facts to Remember

Odd numbers chart (1 to 100).

This chart consists of odd numbers from 1 to 100. You can also practise writing the odd numbers from 1 to 1000 in your notebook.

Odd numbers chart 1 to 100

List of Odd Numbers

There are 25 odd numbers from 1 to 50 while there are 50 in between 1 and 100. In case of numbers from 1 to 1000, there are 500 odd numbers and 500 even numbers.

Odd Numbers from 101 to 200

Odd numbers from 201 to 300, odd numbers from 301 to 400, odd numbers from 401 to 500, properties of odd numbers.

There are four main properties of odd numbers, which are related to their addition, subtraction, multiplication, and division. Each of these properties is discussed in the following points in a detailed way.

Adding Two Odd Numbers

Any odd number added to another odd number always gives an even number. This statement is also proved below.

Let two odd numbers be a and b.

These numbers can be written in the form where

a = 2k 1 + 1

and b = 2k 2 + 1 where k 1 , k 2 ∈ Z

Adding a + b we have,

(2k 1 + 1) + (2k 2 + 1) = 2k 1 + 2k 2 + 2 = 2(k 1 + k 2 + 1) which is surely divisible by 2.

Subtracting Two Odd Numbers

When an odd number is subtracted from an odd number, the resultant number will always be an even number. This is similar to adding two odd numbers where it was proved that the resultant was always an even number.

Multiplication of Two Odd Numbers

If an odd number is multiplied by another odd number, the resulting number will always be an odd number. A proof of this is also given below.

Let two odd number be a and b. These numbers can be written in the form where

a = 2k 1 + 1 and b = 2k 2 + 1 where k 1 , k 2 ∈ Z

Now, a × b = (2k 1 + 1)(2k 2 + 1)

So, a × b = 4k 1 k 2 + 2k 1 + 2k 2 + 1

The above equation can be re-written as:

a × b = 2(2k 1 k 2 + k 1 + k 2 ) + 1 = 2(x) + 1

Thus, the multiplication of two odd number results is an odd number.

Division of Two Odd Numbers

Division of two odd numbers always results in an odd number if and only if the denominator is a factor of the numerator, or else the number result in decimal point number.

If we summarise the properties of odd numbers, we have:

Types of Odd Numbers

There are mainly two types of odd numbers:

  • Consecutive odd numbers
  • C omposite odd numbers

Consecutive Odd Numbers

If ‘a’ is an odd number, then ‘a’ and ‘a + 2’ are called consecutive odd numbers. A few examples of consecutive odd numbers can be

  • 19 and 21 etc.

Even for negative odd numbers, consecutive ones will be:

  • -13 and -11, etc.

Composite Odd Number

A composite odd number is a positive odd integer that is formed by multiplying two smaller positive integers or multiplying the number with one. The composite odd numbers up to 100 are: 9, 15, 21, 25, 27, 33, 35, 39, 45, 49, 51, 55, 57, 63, 65, 69, 75, 77, 81, 85, 87, 91, 93, 95, 99.

What is the Smallest Odd Composite Number?

The smallest odd composite number is 9. As we know, the first few odd numbers are 1, 3, 5, 7, 9, 11, and so on. And we know that the list of the first few composite numbers are 4, 6, 8, 9, 10, 12, 14, and so on. By comparing the definition of both odd numbers and composite numbers, we can conclude that 9 is the smallest odd composite number.

i.e., List of odd numbers: 1, 3, 5, 7, 9 , 11, …

List of composite numbers: 4, 6, 8, 9 , 10, 12, 14, …

Video Lesson on Numbers

odd numbers travel

Solved Examples on Odd Numbers

Find the sum of the smallest and the largest 3 digits odd numbers and also prove that it is divisible by 2.

Smallest 3 digit odd number = 101

Largest 3 digit odd number = 999

Sum of both the numbers = 101 + 999 = 1100

The number 1100 is divisible by 2 (as per the divisibility rule of 2).

This proves that the number is even.

Example 2 :

Are the following numbers odd or even?

  • 32 – 37
  • 25 is not divisible by 2, so odd number.
  • 15 + 13 = 28, divisible by 2, not an odd number
  • 32 – 37 = -5, is an odd number

Fill in the blanks with suitable odd numbers: __, 2, __, 4, __, 6, __, 8, __, 10, __, 12. 22, __, 24, __, 26, __, 28, __, 30. 100, __, 102, __, 104, __, 106, __, 108.

Solution: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 22, 23, 24, 25, 26, 27, 28, 29, 30. 100, 101, 102, 103, 104, 105, 106, 107, 108.

Example 4: How many odd numbers are there between 1 to 100?

Solution: There are 50 odd numbers and 50 even numbers between 1 to 100. Number of odd numbers = 100/2 = 50

Odd Numbers Worksheet

  • Is 7 an even or odd number?

How do you determine if a number is odd or even?

  • Mention all the odd numbers which are greater than 60 and smaller than 120.
  • List all the odd numbers which are greater than -4 and smaller than 20.

Is zero an odd number? Why?

Related articles, frequently asked questions on odd numbers, what is meant by odd numbers.

The numbers which are not divisible by 2, evenly, are called odd numbers. For Example: 3, 5, 17, 19, 21, etc.

What are the first 10 odd numbers?

No, zero is not an odd number but an even number, because, when we divide 0 by 2, it gives us a quotient equal to 0 and also there is no remainder left after division. So, 0 is evenly divided by 2.

Is 37 an odd number or even?

As we can see, the unit place of 37 consists of an odd number i.e. 7, which is not evenly divisible by 2, therefore, it’s an odd number.

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Customize page numbers and their formats in different Word document sections

To use different page numbers or formats in different sections, create Page breaks and set page number for each.

The following shows an intro with lower case Roman numerals. You can use any other format instead.

Select between the intro and the body of the document and go to Layout > Breaks > Next Page .

Tip:  To see section breaks and other formatting marks, go to Home and select Show/Hide (¶) to turn on the display of formatting marks.

In the header for the body section, deselect Link to Previous . If Link to Previous is dimmed, check to make sure a section break was created.

In the intro section select Page Number and choose a location and style. If your change only affects the first page of your section, make sure Different First Page is not selected.

To choose a format or to control the starting number, select Page Number > Format Page Numbers .

Do either or both of the following:

Select Number format to select the format for the numbering, such as a, b, c or i, ii, iii for the intro.

Under Page numbering , choose Start at and type a number that you want to start the section with. For example, restart numbering at the beginning of the body section.

Select Close Header and Footer , or double-click anywhere outside the header or footer area to exit.

Note:  Headers and footers are linked separately, so if your page number is in the header, turn off linking for headers. If your page number is in the footer, turn off linking for footers.

Go to Header & Footer > Page Number , and then click Page Number .

Choose the position and alignment of page numbers. If you don't want a page number to appear on the first page, clear Show number on first page .

To choose a format or to control the starting number, go to Header & Footer > Page Number > Format Page Numbers .

To change the numbering style, select a different style in Number format .

To change the starting page number of the newly created section, select Start at , and then enter a number.

Select OK .

Select Close Header and Footer , or double-click outside of the header or footer to exit.

For more info on page numbers, see Page numbering in Word .

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IMAGES

  1. Odd numbers-Definition, Examples, Worksheet and Properties

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  2. Odd Numbers

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  3. Odd Numbers (Definition, Chart, Properties & Solved Examples)

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  4. Odd Number Charts Printable for Kids

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  5. Why Do Teenage Girls Travel In Odd Number Groups :: Random Images

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  6. List of Odd Numbers 1 to 1000

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COMMENTS

  1. How Airlines Decide On Flight Numbers, And Have Fun While They're At It

    Airlines often use even flight numbers for one direction of travel, and odd flight numbers for another direction, just to keep things consistent; for example, American generally uses even flight numbers for flights headed east or north, and odd flight numbers for flights headed west or south

  2. U.S. Highway Numbering

    North-south routes are assigned odd numbers, with the numbers growing larger from west to east; east-west routes are assigned even numbers, with the numbers growing larger from south to...

  3. Here's the Surprising Logic Behind America's Interstate Highway Numbers

    As the video below points out, I-76 is a highway in Colorado, and it's also the interstate number of the Pennsylvania Turnpike. There are plenty of other examples of this across the U.S. as well ...

  4. Flight Numbers Explained: How Airlines Decide Route Numbers

    Even numbers are outbound from the home country, and odd numbers fly back. (British does it the other way; odd flights are outbound, starting from that BA1 to New York.) The geography-based model is in use at other airlines too: On Alitalia, for example, if your flight is in the 600s you know you're going to the Americas, and in the 700s to Asia.

  5. airlines

    Odd vs even flight numbers Ask Question

  6. What's the Secret Behind the Numbers on the Interstate Signs?

    The number of digits in the name tells you whether an interstate connects more than one city, or if it serves a single metropolitan area. Interstates with one or two digits (e.g., I-95) interconnect several regions. Those with three digits (e.g., I-285), on the other hand, are meant to serve a single city and are called auxiliary interstate ...

  7. States With the Most Interstate Highways and Other Facts About

    Routes with odd numbers travel north and south, while routes with even numbers run east and west. How Interstate Highways Are Named. The American Association of State Highway and Transportation Officials developed a naming system for highways to more easily identify and differentiate them. Interstate highways are named using one- or two-digit ...

  8. Life in the U.S.

    Odd number means the freeway runs north-south, while even numbered freeways travel east and west. For example, interstate 5 (I-5) goes all the way from the Southern border in San Diego to the Northern border in Blaine, WA. I-10, on the other hand, connects the West Coast of San Diego and the East Coast of Jacksonville, FL. ...

  9. United States Numbered Highway System

    Generally, most north-to-south highways are odd-numbered, with the lowest numbers in the east and the highest in the west, while east-to-west highways are typically even-numbered, with the lowest numbers in the north, and the highest in the south, though the grid guidelines are not rigidly followed, and many exceptions exist.

  10. Galileo's law of odd numbers

    The Galileo's law of odd numbers states that the distances traveled are proportional to the squares of the elapsed times. In other words, in equal successive periods of time, the distances traveled by a free-falling body are proportional to the succession of odd numbers ($1, 3, 5, 7,$ etc.).I clearly understand from kinematics equation that the distances traversed in a time interval are ...

  11. Numbering the Highway System

    Seven highways run from border to border: I-5, I-15, I-35, I-55, I-65, I-75, and I-95. The interstate system totals 46,300 miles. All interstate highways are marked by blue signs with red tops. The north-south highways have odd numbers with 1 or 2 digits, usually including a 5.

  12. Understanding even and odd numbers visually

    ( 21 votes) Upvote Flag ichbinzoee 3 years ago You can tell if a number is odd or even by looking at the last digit. In other words, what the number ends in. If the number ends in 2, 4, 6, 8, or 0, then the number is even. If the number ends in 1, 3, 5, 7, or 9, then the number is odd. Let's look at a few examples. Is 10 even or odd?

  13. Intro to even and odd numbers (video)

    mathematically, any number that can be divided by two to create another whole number is even. Zero passes this test because if you halve zero you get zero and Every integer is either of the form (2 × ) + 0 or (2 × ) + 1; the former numbers are even and the latter are odd. For example, 1 is odd because 1 = (2 × 0) + 1, and 0 is even because 0 ...

  14. List of Odd Numbers from 1 to 1,000

    If you're looking for a comprehensive list of odd numbers from 1 to 1,000, this is the place for you! I listed the odd numbers into ten (10) groups. Odd Numbers 1 to 100 Odd Numbers 101 to 200 Odd Numbers 201 to 300 Odd Numbers 301 to 400 Odd Numbers 401 to 500 Odd Numbers 501 to 600 Odd Numbers 601 to 700 Odd Numbers 701 to 800

  15. PDF The Law of Odd Numbers

    The Law of Odd Numbers From his observations and analysis of motion using inclined planes, Galileo discovered a ... He found that any object under the conditions of uniform acceleration would travel distances that would increase by factors according to the odd integers in relation to successive time intervals.

  16. Specialty Dining Reservations for multiple rooms

    You do see reservations available for odd numbers at times. We used to travel as a group of three and I have made reservations for three a few times, but more often than not we had to go for four. It is possible that they have stopped offering them recently, but you certainly used to be able to get the occasional table for odd numbers pre covid

  17. Odd Numbers 1 to 100

    The list of odd numbers from 1 to 100 can be given as follows: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99. Odd Prime Numbers from 1 to 100

  18. Galileo's law of odd numbers

    Explanation Derivation of Galileo's law of odd numbers Using a speed-time graph The graph in the figure is a plot of speed versus time. Distance covered is the area under the line. Each time interval is coloured differently.

  19. Odd Numbers

    Examples: 1, 23, 535, 67, 12763489 Definition of Odd Numbers Odd number can be defined as an integer that is not divisible by "2." These are the numbers that have 1, 3, 5, 7, or 9 at their ones place. Odd numbers are simply the integers that are not multiples of 2. How to Identify Odd Numbers? Let's see how we identify odd numbers.

  20. Odd Numbers

    Odd Numbers. Odd numbers or integers are part of whole numbers that are partially divisible into pairs. Thus all numbers except the multiples of 2 are odd numbers. They are in the form of 2k+1, where k ∈ Z (integers) are called odd numbers. Some examples are 1, 3, 5, 7, and so on. They are just the opposite of even numbers.

  21. Definition, List of Odd Numbers

    In order to find the mean of the first five odd numbers we need to follow the steps listed below: Step 1: List the first five odd numbers, they are 1, 3, 5, 7, and 9. Step 2: Calculate the sum → 1 + 3 + 5 + 7 + 9 = 25. Step 3: Apply the mean formula = Mean of any n numbers = (Sum of n numbers) ÷ n = 25/5 = 5.

  22. Odd Numbers (Definition, Examples) Byjus

    Odd numbers are those numbers that are not completely divisible by 2. The fact is that there is always a remainder when an odd number is divided by 2. The last digit of an odd number is 1, 3, 5, 7, or 9. The set of odd numbers comprises 1, 3, 5, 7, 9, 11, 13, 15, and so on. An odd number can also be defined in terms of whether it can be divided ...

  23. Official Trusted Traveler Program Website

    This is the official U.S. Customs and Border Protection (CBP) website where international travelers can apply for Trusted Traveler Programs (TTP) to expedite admittance into the United States (for pre-approved, low-risk travelers).

  24. Odd Numbers (Definition, Chart, Properties & Solved Examples)

    Math Article Odd Numbers Odd Numbers Odd numbers are the numbers that cannot be divided by 2 evenly. It cannot be divided into two separate integers evenly. If we divide an odd number by 2, then it will leave a remainder. The examples of odd numbers are 1, 3, 5, 7, etc. Odd numbers are just the opposite concept of even numbers .

  25. Customize page numbers and their formats in different Word document

    To choose a format or to control the starting number, select Page Number > Format Page Numbers. Do either or both of the following: Select Number format to select the format for the numbering, such as a, b, c or i, ii, iii for the intro. Under Page numbering, choose Start at and type a number that you want to start the section with.

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