Factors, Multiples & Primes — GCSE Mathematics Revision
Revise Factors, Multiples & Primes for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to Fractions, Decimals & PercentagesWhat is Factors, Multiples & Primes?
A factor divides exactly into a number. A multiple is the result of multiplying a number by an integer. A prime number has exactly two factors: 1 and itself. Prime factorisation means writing a number as a product of its prime factors — for example, 60 = 2² × 3 × 5. You use prime factorisation to find the HCF (highest common factor) and LCM (lowest common multiple).
Step-by-step explanationWorked example
Find the HCF and LCM of 36 and 90. Prime factorise: 36 = 2² × 3², 90 = 2 × 3² × 5. HCF = 2¹ × 3² = 18 (lowest powers of shared primes). LCM = 2² × 3² × 5 = 180 (highest powers of all primes).
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Common mistakes
- 1Forgetting that 1 is NOT a prime number — it only has one factor.
- 2Missing a branch in the factor tree and getting an incomplete prime factorisation.
- 3Confusing HCF and LCM — HCF uses the lowest powers of shared primes, LCM uses the highest powers of all primes.
- 4Not writing the final answer in index form when the question asks for it.
Factors, Multiples & Primes exam questions
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Factors, Multiples & Primes
Core concept
A factor divides exactly into a number. A multiple is the result of multiplying a number by an integer. A prime number has exactly two factors: 1 and itself. Prime factorisation means writing a number…
Frequently asked questions
How do I find HCF and LCM using prime factorisation?
Write each number as a product of prime factors. For HCF, take the lowest power of each shared prime. For LCM, take the highest power of every prime that appears in either factorisation.
Is 1 a prime number?
No. A prime number must have exactly two distinct factors. The number 1 only has one factor (itself), so it is not prime.