# Factors and Multiples

### A factor is a whole number that divides exactly into another whole number.

You can also think of factors as being the numbers that you multiply to get another number,
so 2 and 3 are factors of 6 (and so are 1 and 6).

A good understanding of factors is essential for working with fractions.

## How to find the factors of a number

We'll take 12 as an example.

All numbers have a factor of 1 and the number itself, so you know two factors straight away.

1 and 12.

Next, see if the number will divide by 2. 12 ÷ 2 = 6, so 2 and 6 are also factors.

Next, see if 12 can be divided by 3 ... 12 ÷ 3 = 4 so 3 and 4 are factors.

4 is a factor, so next we see if 12 will divide by 5 - no.

6 is a factor, so we don't have to divide by this.

A factor cannot be more than half of the number so we have found all the factors of 12.

They are 1, 2, 3, 4, 6 and 12.

Notice that they come in pairs which multiply together to form the number.

It is a good idea to work through all the numbers from 1 to 20 and identify all of the factors. Keep the piece of paper that you work on - it will be useful for Prime Numbers.

You should end up with something like:

## Highest Common Factor (HCF)

The Highest Common Factor is the largest number which is shared between two numbers.

### Factors of 12 - 1,2,3,4,6,12 Factors of 20 - 1,2,4,5,10,20

The factors 1, 2 and 4 are shared by 12 and 20, but 4 is the largest. The HCF of 12 and 20 is 4.

# Multiples

## Common Multiples

Common multiples are multiples that numbers have in common.

## Least Common Multiple (LCM)

The least common multiple is the smallest whole number that the numbers share.