Breaking down into prime factors
You learn to split a composite number into a multiplication of prime numbers.
How to work it out
- Write a number as a product of prime numbers (2, 3, 5, 7).
- Divide each time by the smallest prime that goes into it until you get to 1.
A worked example
Factorise 12
- Divide 12 by the smallest prime number: 12 ÷ 2 = 6.
- Divide 6 by 2 again: 6 ÷ 2 = 3.
- The number 3 is already prime.
- The prime factors are 2 × 2 × 3 = 12.
More examples
20 = 2 × 2 × ?
- Multiply the known factors: 2 × 2 = 4.
- Divide the number by 4: 20 ÷ 4 = 5.
- The missing prime factor is 5.
18 = 2 × 3 × ?
- Work out the known factors: 2 × 3 = 6.
- Divide 18 by 6: 18 ÷ 6 = 3.
- The missing prime factor is 3.
Try it yourself
Which prime number is missing at the question mark?
50 = 2 × 5 × ?
Which prime number is missing at the question mark?
28 = 2 × 2 × ?
Watch out
You use a number that is not prime itself, like 4 or 6.
Prime numbers have exactly two factors (1 and itself): 2, 3, 5, 7, 11.
Tips
- Always start by dividing by 2 as long as the number is even, then try 3, 5 and 7.
Why it works
Prime numbers are the building blocks of all numbers. You can write every number in exactly one way as a multiplication of prime numbers (like 2, 3, 5 and 7).