Factors

The factors of a number are any numbers that divide into it exactly. This includes 1 and the number itself.

For example, the factors of 6 are 1, 2, 3 and 6. The factors of 8 are 1, 2, 4 and 8.

For larger numbers it is sometimes easier to ‘pair’ the factors by writing them as multiplications.

For example, 24 = 1 x 24 = 2 x 12 = 3 x 8 = 4 x 6

So the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

Answer

The factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40.

Make sure that you got all of them. Do not forget 1 and 40.

Highest common factor (HCF)

We have already seen that the factors of 24 are

1, 2, 3, 4, 6, 8, 12 and 24

and that the factors of 40 are

1, 2, 4, 5, 8, 10, 20 and 40.

The numbers 1, 2, 4 and 8 appear in both lists, so they are known as the common factors of 24 and 40.

The number 8 is the highest of them, and it is called the highest common factor (HCF).

Answer

The factors of 12 are 1, 2, 3, 4, 6 and 12

The factors of 20 are 1, 2, 4, 5, 10 and 20.

The HCF of 12 and 20 is 4.

The multiples of a number are all the numbers that it will divide into. This includes the number itself.

Look at the lists - multiples are just like times tables.

The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, …

The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, …

The numbers 12, 24 and 36 appear in both lists, so they are known as common multiples.

The number 12 is the lowest number to appear in both lists, and it is called the lowest common multiple (LCM).

Answer

The multiples of 6 are 6, 12, 18, 24, 30, 36, 42…

The multiples of 10 are 10, 20, 30, 40, 50…

The LCM of 6 and 10 is 30.

Now try a Test Bite