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Edexcel IGCSE Maths (4MA1) · Unit 1: Number

IGCSE Maths HCF, LCM and Prime Factors Questions and Answers

HCF, LCM and Prime Factors questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 3 worked examples first, then cover each solution and redo it yourself.

Practise HCF, LCM and prime factors in Unit 1 →HCF, LCM and Prime Factors revision notes

What this topic covers

HCF, LCM and Prime Factors worked examples

Worked example 1: Factors and multiples

List the factors of 36 that are also multiples of 3.

Solution

  1. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
  2. Those divisible by 3: 3, 6, 9, 12, 18, 36.

Answer: 3, 6, 9, 12, 18, 36

Tip: List factors in pairs so none are missed: 1 × 36, 2 × 18, …

Worked example 2: Product of prime factors

Write 1260 as a product of prime factors in index form.

Solution

  1. \(1260=2\times630=2\times2\times315\).
  2. \(315=3\times105=3\times3\times35=3\times3\times5\times7\).
  3. So \(1260=2^2\times3^2\times5\times7\).

Answer: \(2^2\times3^2\times5\times7\)

Tip: Keep dividing by the smallest prime that works.

Worked example 3: HCF and LCM

Find the HCF and LCM of 84 and 90.

Solution

  1. \(84=2^2\times3\times7\) and \(90=2\times3^2\times5\).
  2. HCF: lowest powers of common primes, \(2\times3=6\).
  3. LCM: highest powers of all primes, \(2^2\times3^2\times5\times7=1260\).

Answer: HCF 6, LCM 1260

Tip: Check: HCF × LCM = 84 × 90.

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

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Questions students ask

Which Edexcel IGCSE Maths papers test HCF, LCM and prime factors?

Either Higher tier paper, 1H or 2H, can test HCF, LCM and prime factors: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more HCF, LCM and prime factors questions?

In the IGCSE student hub: Unit 1 (Number) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

More Unit 1 topics: Number