# What Is an Odd Number?

Odd numbers are integers that cannot be divided exactly by 2.

#### Dictionary Definition

The Oxford English Dictionary defines an even number as a number "having one left over as remainder when divided by two. Opposed to even."

# Examples of Odd Numbers

Some examples of odd numbers are given below:

# Odd Numbers on a Number Line

The image below shows the odd numbers on the number line.

# How to Check if a Number Is an Odd Number

A number is odd if it cannot be divided exactly by 2. If it is divided by 2, the answer will not be a whole number. There will be a remainder of 1.

#### An Example Question

Is 25 an odd number?
Step 1
Divide the number by 2.
25 ÷ 2 = 12.5 = 12 r 1
Step 2
Check if the answer from Step 1 is a whole number. If it is not, and there is a remainder of 1, the original number is odd. Else it is even.

In our example, 12.5 is not a whole number.

25 is an odd number.

# A Formula to Generate Odd Numbers

The formula below generates odd numbers:

If k takes a whole number (1, 2, 3...), then n will always be odd.
k = 0 ∴ n = 2k + 1 = 2 × 0 + 1 = 1
k = 1 ∴ n = 2k + 1 = 2 × 1 + 1 = 3
k = 2 ∴ n = 2k + 1 = 2 × 2 + 1 = 5
k = 3 ∴ n = 2k + 1 = 2 × 3 + 1 = 7
k = 4 ∴ n = 2k + 1 = 2 × 4 + 1 = 9

# A Real Example of Odd Numbers

The slider below shows a real example of odd numbers:
##### Interactive Test
show

Here's a second test on odd numbers.
Here's a third test on odd numbers.
Here's a dynamic test on odd numbers.

# A Quick Way to See If a Number Is Odd

A number is odd if its last digit is 1, 3, 5, 7 or 9.

# Even Numbers

If a number isn't odd, it is even.

An even number is a whole number that can be divided exactly by 2.

A number is even if its last digit is 0, 2, 4, 6 or 8.

The formula below generates even numbers:

If k takes a whole number (1, 2, 3...), then n will always be even.