# What Is an Odd Number? (Mathematics Lesson)

# 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

25 ÷ 2 = 12.5 = 12 r 1

Step 2

**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

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.

##### Top Tip

# 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.##### Note

# 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.