Year 8: Prime factorisation

Prime factorisation is a way of breaking down a number into its simplest prime number components. It's like building a number using only prime numbers.

What are Prime Numbers?

A prime number is a whole number greater than 1 that has only two factors (divisors): 1 and itself. Examples: 2, 3, 5, 7, 11, 13...

How to Prime Factorise:

1. Start with the smallest prime number, 2. Can 2 divide evenly into the number? If yes, divide and write 2 down.
2. Continue dividing by 2 until you can no longer do so evenly.
3. Move to the next prime number, 3. Can 3 divide evenly into the remaining number? If yes, divide and write 3 down.
4. Repeat the process with the new number until you have completely broken it down into prime numbers.

Example: Prime factorising 36

36 = 2 x 18

18 = 2 x 9

9 = 3 x 3

Therefore, the prime factorisation of 36 is 2 x 2 x 3 x 3 or 2² x 3²

Important Notes:

• Always start with the smallest prime number.
• Keep dividing until you have only prime numbers left.
• Remember that 1 is not a prime number.