GCSE & IGCSE maths practice

Prime factorisation questions and answers

Every whole number above 1 can be written as a product of prime numbers in exactly one way. Use a factor tree (or keep dividing by primes) and write the answer in index form, like $72 = 2^3 \times 3^2$ . Type the powers of each prime in the boxes.

8 questions · Foundation tier · Every answer is checked as you type it, with a full worked solution. Updated 27 Oct 2026.

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Where prime factorisation comes up

GCSE (AQA, Edexcel, OCR)	Foundation and Higher: prime factorisation, including product notation and index form, and the unique factorisation theorem.
Cambridge IGCSE (0580)	Core and Extended: identify and use prime numbers and prime factors, including writing a number as a product of prime factors.

The method

Split the number into two factors, then keep splitting until every branch ends in a prime.
Collect equal primes as powers: 2 × 2 × 2 = 2³.
Write in index form, smallest prime first.
Check by multiplying back.

Prime factorisation questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upFoundation

$60 = 2^a \times 3^b \times 5^c$ . Find $a$ , $b$ and $c$ .

a =b =c =

Question 2Warm-upFoundation

$72 = 2^a \times 3^b$ . Find $a$ and $b$ .

a =b =

Exam-style

Question 3Exam-styleFoundation

$100 = 2^a \times 5^b$ . Find $a$ and $b$ .

a =b =

Question 4Exam-styleFoundation

Which is 84 written as a product of its prime factors?

Question 5Exam-styleFoundation

$360 = 2^a \times 3^b \times 5^c$ . Find $a$ , $b$ and $c$ .

a =b =c =

Question 6Exam-styleFoundation

$450 = 2^a \times 3^b \times 5^c$ . Find $a$ , $b$ and $c$ .

a =b =c =

Challenge

Question 7ChallengeFoundation

Find the HCF of $2^3 \times 3 \times 5$ and $2^2 \times 3^2$ .

Question 8ChallengeFoundation

What is the smallest whole number you can multiply 72 by to make a square number?

Common mistakes

Stopping at a non-prime like 4 or 9.
Including 1 as a prime factor.
Forgetting to write powers in index form.

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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Where prime factorisation comes up

The method

Prime factorisation questions

Warm-up

Exam-style

Challenge

Common mistakes

Stuck on one of these?

More maths questions

Sources

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