Example 1 · level 1 — a gentle start
Which of these is a prime number?
- 2
- 8
- 9
- 10
Answer: 2 — 2 has no factors except 1 and itself, so it is prime.
11+ factors and primes questions
Factors and primes comes up in the maths paper of every major 11+ format. Here is what the questions look like, the method that works under time pressure, and five worked examples with the full reasoning, from a gentle start to a hard paper.
Maths · examined by GL and CEM · 5 worked examples
What your child needs to know
- A factor divides into a number exactly, with nothing left over.
- A prime number has only two factors: 1 and itself.
Where marks get lost: The highest common factor is the biggest one two numbers share.
Worked examples
Every question below is generated by the same engine your child practises on, and every answer is derived by our checker rather than written by hand — which is why we can put them on a public page at all.
Example 2 · level 2 — typical of early practice
Which of these is a prime number?
- 7
- 16
- 14
- 6
Answer: 7 — 7 has no factors except 1 and itself, so it is prime.
Example 3 · level 3 — standard paper difficulty
What is the highest common factor of 18 and 17?
- 2
- 17
- 306
- 1
Answer: 1 — The largest number that divides both 18 and 17 is 1.
Example 4 · level 4 — a harder paper
What is the highest common factor of 14 and 25?
- 14
- 11
- 1
- 350
Answer: 1 — The largest number that divides both 14 and 25 is 1.
Example 5 · level 5 — the level that separates candidates
What is the lowest common multiple of 13 and 38?
- 25
- 494
- 13
- 1
Answer: 494 — The smallest number both 13 and 38 divide into is 494.
How to practise this at home
- Work in short, frequent sessions. Ten minutes daily beats an hour at the weekend, because the recall gap is what builds memory.
- Insist on written working, even for questions your child can do in their head — under exam pressure the method is what survives.
- When an answer is wrong, ask them to explain their reasoning before you correct it. The error is almost always in one step, not the whole approach.
Practise factors and primes with a tutor that explains
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