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Prime Factorisation using Factor Tree

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

      = 26

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.

factor tree for 45

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 32