A number that is able to divide exactly into another number is known as a factor of that number.

For example, factors of the number 8 are 1, 2, 4 and 8.

To figure out factors of larger numbers it can help to pair off numbers that multiply to make that number.

For example, factors of 36:

1 x 36 2 x 18 3 x 12 4 x 9 6 x 6

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Highest common factor (HCF)

A common factor is one shared by two or more numbers for example:

The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18 and 36

The factors of 45 are: 1, 3, 5, 9, 15 and 45

The common factors between 36 and 45 are 1, 3 and 9.

The highest common factor (HCF) is 9.

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Least common multiples (LCM)

If you have a list of numbers, the least common multiple is the smallest common multiple in the list

For example, the multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18 etc.

While the multiples of 3 are: 3, 6, 9, 12, 15, 18, 21 etc.

The common multiples are 6, 12 and 18.

The least common multiple (LCM) is 6.

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Multiples

A multiple of a number is one that the number is able to divide into.

For example, multiples of 3 are: 3, 6, 9, 12, 15 and so on.

The multiples of 7, on the other hand, are 7, 14, 21, 28 and so on.

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Prime factors

All numbers can be figured out as a product of prime number.

For example:

24 = 2 x 2 x 2 x 3

252 = 2 x 2 x 3 x 3 x 7

If you’re asked in an exam to write a number as a product of tis prime factors there are two methods you can use.

For example: write 36 as a product of its prime numbers.

First of all take the smallest prime number that divides into 36: 2. Therefore, we can write 36 as:

18 x 2 = 36

Now, figure out the smallest prime number that divides into 36: 2 again. So, you can write:

9 x 2 x 2 = 36

Again, figure out the smallest prime number to divide into 9: 3

So, the answer is:

3 x 3 x 2 x 2 = 36

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Highest common factor and lowest common multiple

Prime factors can be used to figure out the HCF and LCM.

For example, take 36 and 45:

36 = 2 x 2 x 3 x 3

54 = 2 x 3 x 3 x 3

If you take the common numbers from both and multiply them together then you’ll get the HCF:

2 x 3 x 3 = 18

To find the LCF, you look at which list as the most of which factor

36 = (2 x 2) x (3 x 3)

54 = 2 x (3 x 3 x 3)

36 has the most 2s and 54 has the most 3s.

So, LCM: (2 x 2) x (3 x 3 x 3) = 4 x 27 = 108