# Odd Numbers

## 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.

### Question

Is 25 an odd number?

### Step-by-Step:

# 1

Divide the number by 2.

25 ÷ 2 = 12.5 = 12 r 1

# 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.

### Answer:

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