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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
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
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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.