GCSE Mathematics Revision — Factors, Multiples & Primes
Revise Factors, Multiples & Primes for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP.
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What 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 examples
Worked example 1: Core method
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).
Worked example 2: Exam variation
Now change one detail in the question and keep the same structure: name the Factors, Multiples & Primes idea being tested, show the method or evidence, then explain why it answers the command word. This helps GCSE Mathematics students avoid memorising one surface pattern.
Worked example 3: Mark-scheme check
Finish by checking the answer against marks: one point for the correct Factors, Multiples & Primes idea, one for accurate working or evidence, and one for a precise final statement. If any step is vague, rewrite it before moving to timed practice.
Mini lesson for Factors, Multiples & Primes
1. Understand the core idea
A factor divides exactly into a number. A multiple is the result of multiplying a number by an integer.
Can you explain Factors, Multiples & Primes without copying the notes?
2. Turn it into marks
Find the HCF and LCM of 36 and 90. Prime factorise: 36 = 2² × 3², 90 = 2 × 3² × 5.
Underline the method, evidence, or command-word move that would earn credit in GCSE Number.
3. Fix the likely mark leak
Watch for this mistake: Forgetting that 1 is NOT a prime number — it only has one factor.
Write one correction rule before doing another practice question.
Practise this topic
Start with low-focus cards for Factors, Multiples & Primes, then move into full exam-style practice when you want the heavier session.
Mini quiz: Factors, Multiples & Primes
Three quick checks for revision practice. They are original StudyVector prompts, not official exam-board questions.
Question 1
In one GCSE sentence, explain what Factors, Multiples & Primes is testing.
Answer: A factor divides exactly into a number. A multiple is the result of multiplying a number by an integer.
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Factors, Multiples & Primes question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Forgetting that 1 is NOT a prime number — it only has one factor." What should their next repair task be?
Answer: Do one Factors, Multiples & Primes question and review the mistake type.
Mark focus: Error correction and next-step practice.
Factors, Multiples & Primes flashcards
Core idea
What is the main idea in Factors, Multiples & Primes?
A factor divides exactly into a number. A multiple is the result of multiplying a number by an integer.
Common mistake
What mistake should you avoid in Factors, Multiples & Primes?
Forgetting that 1 is NOT a prime number — it only has one factor.
Practice
What is one useful practice task for Factors, Multiples & Primes?
Answer one Factors, Multiples & Primes question and review the mistake type.
Exam board
How should you use board notes for Factors, Multiples & Primes?
Use your own GCSE specification for exact paper wording and depth.
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
Exam-style questions for Factors, Multiples & Primes with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP specifications.
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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.