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:

Number | Factors
1 | 1
2 | 1,2
3 | 1,3
4 | 1,2,4
5 | 1,5
6 | 1,2,3,6
and so on

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.

The multiples of a number are the results of multiplying the number by other numbers or put another way, all the numbers that it will divide into.

Multiples are just Times Tables

The multiples of 2 are 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30 ....
The multiples of 3 are 3,6,9,12,15,18,21,24,27,30,33,36,39,42 .......
The multiples of 4 are 4,8,12,16,20,24,28,32,36,40,44,48,52 ........
The multiples of 5 are 5,10,15,20,25,30,35,40,45,50,55,60,65 ......

Common Multiples

Common multiples are multiples that numbers have in common.

Common multiples of 2 and 3 are : 6, 12, 18, 24, 30, 36 .....
Common multiples of 2 and 4 are : 4, 12, 18, 24, 30, 36 .....
Common multiples of 2 and 5 are : 10,20,30,40,50,60 .......

Least Common Multiple (LCM)

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

Least common multiple of 2 and 3 is 6 (see above)
Least common multiple of 2 and 5 is 10 (see above)
Least common multiple of 2, 3 and 4 is 12 (see above)

These practice papers are graded in difficulty and are designed to build confidence and highlight problems before moving on to the 'official' papers. There are 5 papers of each type which are graded in difficulty.