DfE statement N4 · Number
Factors, multiples, primes, HCF and LCM
Factors, multiples, primes, HCF and LCM is content statement N4 of the DfE GCSE mathematics subject content, in the number area. It is on both tiers, and it is examined without a calculator. Below is what the specification actually requires, the 4 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.
What the specification says
The DfE subject content for GCSE mathematics states, verbatim: "Use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation theorem." (statement N4). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
Tier
Both tiers. This statement is Foundation content, which means Higher students are examined on it too — Higher is Foundation plus more, never instead of it.
Calculator
This is non-calculator territory. Questions on it belong naturally on Paper 1, where written method is all you have — so practise it that way rather than with a calculator to hand.
Common mistakes
- Calling 1 a prime number, or refusing 2 because it is even. A prime has exactly two factors; 1 has one, and 2 has exactly two.
- Swapping factors and multiples — the factors of 12 are the numbers that divide into it, the multiples are 12, 24, 36 and so on.
- Swapping the HCF and the LCM. The HCF cannot be larger than either number; the LCM cannot be smaller than either.
- Leaving a composite number in a prime factorisation, writing 24 = 4 × 6 or 2³ × 4 rather than 2³ × 3.
Sample questions (10 of 30)
Nearby statements
Questions people ask
Is factors, multiples, primes, HCF and LCM on Foundation or Higher?
Both. It is Foundation content, so it can be asked on either tier.
Can I use a calculator for factors, multiples, primes, HCF and LCM?
Not on Paper 1, which is where this normally appears. Paper 1 is non-calculator for both tiers and carries the same 80 marks as each of the other two papers.
How do I find the HCF and LCM from a prime factorisation?
Write both numbers as products of primes. For the HCF take the lower power of each prime that appears in both; for the LCM take the higher power of every prime that appears in either. A Venn diagram of the prime factors does the same job: the overlap multiplies to the HCF and the whole diagram multiplies to the LCM.
What is the single most common mistake here?
Calling 1 a prime number, or refusing 2 because it is even. A prime has exactly two factors; 1 has one, and 2 has exactly two.
Are these past paper questions?
No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.
Back to Number at Foundation or at Higher.