The list of prime numbers starts as follows:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37........

In this activity, we will write numbers as the products of prime factors.

This is known as **prime factorisation.**

__Method__

All whole numbers, other than primes and the number 1, can be written as the product of their prime factors.

We find the prime factors of a number by successively dividing the number by its factor pairs.

Here is an example of a factor tree for the number 36, so that you can picture what they look like..

36 has been split into its factor pair of 4 and 9.

4 has been split into its factor pair of 2 and 2. Both are prime numbers, so they have been circled.

9 has been split into its factor pair of 3 and 3. Both are prime numbers, so they have been circled.

So, the prime factors of 36 are 2, 2, 3 and 3.

36 as a product of its prime factors is: 3 x 3 x 2 x 2

We can tidy this up using indices to make 3² x 2²

Here are a few examples of numbers that have been broken down by prime factorisation:

54 = 2 x 3 x 3 x 3 = 2 x 3^{3}

28 = 2 x 2 x 7 = 2^{2} x 7

24 = 2 x 2 x 2 x 3 = 2^{3} x 3

Let's have a go at some questions now.

You can look back to this explanation at any time during the activity by clicking on the red button at the side of the screen.