Prime factor trees: worked example
22 October 2026
Prime factor trees help children break down numbers into their building blocks, called prime factors. This method is a key skill for 11+ maths and makes larger numbers less intimidating. It's a simple process that shows exactly how a number is made from smaller parts.
Worked example
Factorise 36 into its prime factors using a prime factor tree.
Step 1: Split 36 into two factors. For example, 6 and 6.
Step 2: Split each 6 into two factors. 6 splits into 2 and 3. Both 2 and 3 are prime numbers.
Step 3: Now all the numbers at the ends are prime numbers: 2, 3, 2, and 3.
The answer is 2 × 2 × 3 × 3.
| Number | Split into | Prime? |
|---|---|---|
| 36 | 6 × 6 | No |
| 6 | 2 × 3 | No |
| 6 | 2 × 3 | No |
| 2 | - | Yes |
| 3 | - | Yes |
| 2 | - | Yes |
| 3 | - | Yes |
Key insight: Once your child can spot when all the ends of the tree are prime numbers, they have cracked the method. They'll now recognise prime factor trees in 11+ questions and know how to solve them. The next step is to practise with similar questions and build confidence.
