Prime Factorisation

Prime Factorisation

Basic GCSE(F)

Finding the factors of a number is called Factorising. In addition to the numbers 1 and itself, factors of a number can often be factorised themselves.

Any number can be factorised into a set of prime numbers: this is known as the Product of the Prime Factors, or the Product of its Primes. The number 24

• can be written as 4 x 6,

• which can then be written as (2 x 2) x (2 x 3).

The Product of the Prime Factors for 24 is 23 x 3.

A Prime Factor Tree can be used to obtain the Product of its Primes for a number. Start with the number. Create a pair of branches: at the end of each branch, enter any pair of factors for the number. Repeat the process for each of these factors, but branches are not drawn from prime numbers. Multiply together the primes at the end of each branch.

prime factor tree for 90

90 = 2 x 5 x 3 x 3, re-arrange to:

90 = 2 x 3 x 3 x 5, re-write as powers

90 = 2 x 32 x 5

Examples

1. Write 48 as the product of its primes.

Answer: 48 = 24 x 3.

prime factor tree for 48

2. Write 144 as the product of its primes.

Answer: 144 = 24 x 32

prime factor tree for 144