Edexcel International GCSE Maths Factors, Multiples and Primes Past Paper Questions and Solutions (4MA1 Higher)

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Edexcel International GCSE Maths A (4MA1) · Higher · Numbers and the Number System

Integers, Factors, Multiples and Primes: Edexcel 4MA1 Past Paper Questions and Worked Solutions

This page collects every integers, factors, multiples and primes question from the Pearson Edexcel International GCSE Mathematics A (4MA1) Higher tier Paper 1H and Paper 1HR, January 2020 to June 2025: 12 questions worth 38 marks. Questions run from easier to harder. Try each one first, then click “Show solution” for a step-by-step method with the reason for every step. All answers are checked against the official Pearson mark schemes.

13 marksHigherJune 2023 · Paper 1HR (4MA1/1HR) · Q1

Write 2250 as a product of powers of its prime factors. Show your working clearly.

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  1. Keep dividing by prime numbers: 2250 ÷ 2 = 1125, 1125 ÷ 3 = 375, 375 ÷ 3 = 125, 125 ÷ 5 = 25, 25 ÷ 5 = 5, 5 ÷ 5 = 1
  2. So 2250 = 2 × 3 × 3 × 5 × 5 × 5
  3. Write repeated factors as powers.

Answer: 2 × 32 × 53

22 marksHigherJune 2025 · Paper 1HR (4MA1/1HR) · Q1

Find the lowest common multiple (LCM) of 45 and 70.

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  1. Write each number as a product of prime factors: 45 = 32 × 5 and 70 = 2 × 5 × 7
  2. The LCM uses every prime that appears, each with its highest power: 2 × 32 × 5 × 7
  3. 2 × 9 × 5 × 7 = 630

Answer: 630

32 marksHigherJanuary 2020 · Paper 1H (4MA1/1H) · Q2

Find the lowest common multiple (LCM) of 28 and 105.

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  1. 28 = 22 × 7 and 105 = 3 × 5 × 7
  2. LCM: every prime with its highest power: 22 × 3 × 5 × 7 = 4 × 105

Answer: 420

44 marksHigherJune 2022 · Paper 1H (4MA1/1H) · Q3

(a) Find the highest common factor (HCF) of 56 and 84. Show your working clearly. (2)

(b) Find the lowest common multiple (LCM) of 60 and 72. Show your working clearly. (2)

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Part (a)

  1. 56 = 23 × 7 and 84 = 22 × 3 × 7
  2. HCF: the shared primes with their lowest powers: 22 × 7

Answer: 28

Part (b)

  1. 60 = 22 × 3 × 5 and 72 = 23 × 32
  2. LCM: every prime with its highest power: 23 × 32 × 5 = 8 × 9 × 5

Answer: 360

52 marksHigherJune 2024 · Paper 1H (4MA1/1H) · Q3

Find the highest common factor (HCF) of 72 and 108. Show your working clearly.

Show solution
  1. Write each number as a product of prime factors.
  2. 72 = 2 × 2 × 2 × 3 × 3 = 23 × 32
  3. 108 = 2 × 2 × 3 × 3 × 3 = 22 × 33
  4. The HCF uses only the primes the two numbers share, each with its lowest power: 22 × 32
  5. 22 × 32 = 4 × 9

Answer: 36

Tip: “Working required” means a correct answer with no method may score 0. Always show the prime factor trees or factor lists.
64 marksHigherJanuary 2022 · Paper 1HR (4MA1/1HR) · Q6

(a) Work out the lowest common multiple (LCM) of 36 and 120 (2)

A = 52 × 74 × 11p and B = 5m × 7n−5 × 11, where m, n and p are integers such that m > 2, n > 10 and p > 1

(b) Find the highest common factor (HCF) of A and B. Give your answer as a product of powers of its prime factors. (2)

Show solution

Part (a)

  1. 36 = 22 × 32 and 120 = 23 × 3 × 5
  2. LCM = 23 × 32 × 5 = 8 × 9 × 5

Answer: 360

Part (b)

  1. The HCF uses the lower power of each prime.
  2. 5: m > 2, so 52 is the lower power. 7: n − 5 > 5, so 74 is lower. 11: p > 1, so 111 is lower.

Answer: 52 × 74 × 11

73 marksHigherNovember 2021 · Paper 1H (4MA1/1H) · Q7

Write 3.6 × 103 as a product of powers of its prime factors. Show your working clearly.

Show solution
  1. 3.6 × 103 = 3600
  2. 3600 = 36 × 100 = (22 × 32) × (22 × 52)
  3. Collect the powers of each prime.

Answer: 24 × 32 × 52

84 marksHigherJune 2023 · Paper 1H (4MA1/1H) · Q8

(a) Write 300 as a product of its prime factors. Show your working clearly. (2)

A = 2 × 2 × 2 × 3 × 3 × 5 and B = 2 × 2 × 3 × 3 × 3 × 5

(b) Find the lowest common multiple (LCM) of 5A and 7B. Show your working clearly. (2)

Show solution

Part (a)

  1. Divide by primes: 300 = 2 × 150 = 2 × 2 × 75 = 2 × 2 × 3 × 25 = 2 × 2 × 3 × 5 × 5

Answer: 22 × 3 × 52

Part (b)

  1. 5A = 23 × 32 × 52 and 7B = 22 × 33 × 5 × 7
  2. The LCM takes every prime with its highest power: 23 × 33 × 52 × 7
  3. 8 × 27 × 25 × 7 = 37 800

Answer: 37 800 (= 23 × 33 × 52 × 7)

94 marksHigherJanuary 2021 · Paper 1HR (4MA1/1HR) · Q9

A = 28 × 35 × 114 and B = 26 × 3 × 118

(a) Find the highest common factor (HCF) of A and B. (2)

(b) Find the lowest common multiple (LCM) of 2A and 3B. Give the LCM as a product of powers of its prime factors. (2)

Show solution

Part (a)

  1. Lowest power of each prime: 26, 31, 114

Answer: 26 × 3 × 114

Part (b)

  1. 2A = 29 × 35 × 114 and 3B = 26 × 32 × 118
  2. Highest power of each prime: 29, 35, 118

Answer: 29 × 35 × 118

103 marksHigherJune 2020 · Paper 1H (4MA1/1H) · Q10

A = 2 × 343 and B = 16 × 337

(a) Find the highest common factor (HCF) of A and B. (1)

(b) Express the number A × B as a product of powers of its prime factors. Give your answer in its simplest form. (2)

Show solution

Part (a)

  1. Write 16 as 24, so B = 24 × 337. The HCF uses the lowest powers: 21 and 337.

Answer: 2 × 337

Part (b)

  1. A × B = 2 × 343 × 24 × 337 = 21+4 × 343+37

Answer: 25 × 380

114 marksHigherJune 2024 · Paper 1HR (4MA1/1HR) · Q11

A = 25 × 5 × 72 and B = 23 × 53 × 74

(a) Write down the highest common factor (HCF) of 5A and 2B. Give your answer as a product of prime factors. (2)

(b) Work out the value of (AB)2. Give your answer as a product of prime factors. (2)

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Part (a)

  1. 5A = 25 × 52 × 72 (one more 5) and 2B = 24 × 53 × 74 (one more 2).
  2. The HCF takes each prime with its lowest power: 24, 52 and 72

Answer: 24 × 52 × 72

Part (b)

  1. AB: add the powers of each prime. 25+3 × 51+3 × 72+4 = 28 × 54 × 76
  2. Squaring doubles every power.

Answer: 216 × 58 × 712

123 marksHigherJune 2022 · Paper 1HR (4MA1/1HR) · Q12

P = 33 × 52 × 7 and Q = 32 × 5 × 72

(a) Write down the highest common factor (HCF) of P and Q. (1)

(b) Work out the value of P3 × Q. Give your answer in the form 3x × 5y × 7z where x, y and z are positive integers. (2)

Show solution

Part (a)

  1. Take each prime with its lowest power: 32, 51, 71

Answer: 32 × 5 × 7 (= 315)

Part (b)

  1. P3: multiply every power by 3: 39 × 56 × 73
  2. Multiply by Q: add the powers of each prime: 39+2 × 56+1 × 73+2

Answer: 311 × 57 × 75

More Numbers and the Number System questions

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