# maths revision notes

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My maths revision guide

Prime numbers

Prime numbers are special numbers that can only be divided by themselves and 1.

The first ten prime numbers are  {2},  {3},  {5},  {7},  {11},  {13},  {17},  {19},  {23} and  {29}.

Remember: 'product' means 'times' or 'multiply'

EXAMPLES:

19 is a prime number. It can only be divided by 1 and 19.

9 is not a prime number. It can be divided by 3 as well as 1 and 9

The prime numbers below 20 are: 2, 3, 5, 7, 11, 13, 17, 19

Don't forget: the number 1 is not thought of as a prime number

5 can only be divided exactly by 1 or 5, so it is a prime number

For example 40 = 2 x 2 x 2 x 5

126 = 2 x 3 x 3 x 7

28 = 2 x 2 x 7

Factors

The factors of a number are any numbers that divide into it exactly. T

his 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.

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

The factors of  {10} are  {1},  {2},  {5} and  {10}.

The factors of  {11} are  {1} and  {11} (so  {11} is a prime number)

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.

Multiples

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

Multiples are really just extended times tables.

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…

The multiples of 2 are all the numbers in the 2 times table, such as 2, 4, 6, 8, 10 and so on.

Multiples of 2 always end with a 2, 4, 6, 8 or 0. You can tell 2286, for example, is a multiple of 2 because it ends with a 6.

The multiples of 5 are all the numbers in the 5 times table, such as 5, 10, 15, 20, 25 and so on.

Multiples of 5 always end with a 5 or a 0. You can tell 465, for example, is a multiple of 5 because it ends with a 5.

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

Common factors

Factorising an expression simplifies it in some way. Factorising is the reverse of expanding brackets.

When multiplying out 3(4x - 7), the rule was to multiply everything in the brackets by 3

This gives 3(4x