# What Is a Factor?

## What Is a Factor?

A factor is a number which divides exactly into another number.

The numbers that are multiplied together to make another number are factors.

### Dictionary Definition

The Oxford English Dictionary defines a factor as "each of two or more whole numbers or quantities which, when multiplied together, produce a given number or expression."

## A Real Example of Factors

It is easier to understand factors with an example.

If we multiply 2 and 5 together, the answer is 10. 2 and 5 are factors of 10.

If we multiply 1 and 10 together, the answer is 10. 1 and 10 are also factors of 10.

The factors of 10 are:

## Dividing by Factors

We have seen that 1,2, 5 and 10 are factors of 10.

All of these numbers divide exactly into 10:

10 ÷ 1 = 10

10 ÷ 2 = 5

10 ÷ 5 = 2

10 ÷ 10 = 1

Note: When we divide a number by one of its factors, the answer is another factor.

# More Real Examples of Factors

• The factors of 6 are the numbers that multiply together to make 6.

1 × 6 = 6

2 × 3 = 6

The factors of 6 are:

• The factors of 18 are the numbers that multiply together to make 18.

1 × 18 = 18

2 × 9 = 18

3 × 6 = 18

The factors of 18 are:

• The factors of 48 are the numbers that multiply together to make 48.

1 × 48 = 48

2 × 24 = 48

3 × 16 = 48

4 × 12 = 48

6 × 8 = 48

The factors of 48 are:

## How to Find the Factors of a Number

To find the factors of a number, find the numbers that divide exactly into it.