Prime numbers

Key facts to remember:

  • Prime numbers do not divide by anything except themselves and 1
  • All prime numbers end in 1, 3, 7, or 9

How to find out if a chosen number is a prime number:

  • Does the number end in a 1, 3, 7 or 9?
  • If so, can it be divided by any of the prime numbers that are smaller than its square root?
  • If not, then it is a prime number


Is 83 a prime number?

It ends in a 3, so it could be

The square root of 83 is 9.11 (to 3 s.f.) Prime numbers smaller than 9.11 are 2, 3, and 7. 83 cannot be divided by 2, 3, or 7 so 83 is a prime number.


Key fact:

Factors of a number are all the numbers that divide into it

Finding all the factors of a given number

Example, find all the factors of 24

1 x 24

2 x 12

3 x 8

4 x 6

5 x –

6 x 4

List the factors in pairs, starting with 1 x the number itself. Work your way through methodically, trying 1, 2, 3,…

If you come to a number that won’t divide, put a dash by it, like 5 in the example above

Once a number is repeated, like 4 in the example, you have found all the factors

Prime factors

To find a number as a product of its prime factors, use a factor tree.

Start with your number at the top, split it into two factors, split each factor until you get a prime factor


Multiples of a number are the number multiplied by another number.

For example, some multiples of 12 are 24, 36, 48, 60, 72, 84, 96, 108, 120, ……and so on

Primes, factors and multiples revision questions