# Maths- Factors

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## 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.

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## Highest Common Factor

Here are the list of prime factors of 24 and 36:

24 = 2 x 2 x 2 x 3

36 = 2 x 2 x 3 x 3

If we write down the numbers that are the same in both lists, they will give us the highest common factor of 24 and 36:

HCF of 24 and 36 is 2 x 2 x 3 = 12

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## Lowest Common Multiple

To find the lowest common multiple, we need to think about which list has the most of each factor.

24 = (2 x 2 x 2) x (3)

36 = (2 x 2)    x (3 x 3)

24 has the most 2s. (it has three 2s). And 36 has the most 3s (it has two 3s).

So the LCM of 24 and 36 is (2 x 2 x 2) x (3 x 3) = 72.

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## Multiples

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

• For example, the multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16…
• The multiples of 5 are 5, 10, 15, 20, 25, 30, 35…
• The multiples of 20 are 20, 40, 60, 80, 100…

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

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