NUMBER

Prime Factorisation

Learn the reliable method for prime factorisation, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Prime factorisation writes a number as a product of prime numbers.

Picture itFind every factor pair
2 · THE METHOD

Follow these steps

  1. Divide by the smallest prime factor that works.
  2. Keep splitting every composite factor until all the factors are prime.
  3. Multiply the prime factors to check that they recreate the original number.
3 · WORKED EXAMPLES

See the method in action

Example 1

Which expression is the prime factorisation of 735?

  1. 735 ÷ 7 ÷ 7 ÷ 3 = 5.
  2. Thus 735 = 7 × 7 × 3 × 5, and each factor is prime.
Answer: 7 × 7 × 3 × 5
Example 2

294 = 7 × 7 × 2 × p, where p is prime. What is p?

  1. 294 ÷ 7 ÷ 7 ÷ 2 = 3.
  2. Thus 294 = 7 × 7 × 2 × 3, and each factor is prime.
Answer: 3
4 · ELEVENSPRINT TIP

A useful shortcut

Multiply the prime factors to check that they recreate the original number.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.