Every composite number can be expressed as a product of prime factors. This process – called prime factorisation – leads to expression of composite numbers in the form of index notations when the prime factor repeats itself.

**Example 1**: 21 can be written as 7 x 3

**Example 2**: 64 can be written as

64 = 2 x 32

= 2 x 2 x 16

= 2 x 2 x 2 x 8

= 2 x 2 x 2 x 2 x 4

= 2 x 2 x 2 x 2 x 2 x 2

= 2^{6}

So 64 can be expressed in index form using the prime factor of 2

**Example 3**: 90 can be written as

90 = 2 x 45

= 2 x 5 x 9

= 2 x 5 x 3 x 3

This process of splitting a number as a product of prime numbers is called prime factorisation, and can be shown pictorially below.

This representation is called a * “Factor Tree”* when we repeatedly divide the number by prime numbers until we cannot divide any further.

The factorisation of the number 90 can be written mathematically as

90 = 2 x 5 x 3 x 3

= 2 x 5 x 3^{2}