plumiPrimes, factors and multiples: AQA GCSE Maths questions
Every AQA GCSE Maths exam question on N4 Primes, factors and multiples, 2017–2025, with its mark scheme and examiner’s report.
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All 28 questions on Primes, factors and multiples, as a list
- June 2025, Paper 2H, Q1 (3 marks): (a) Work out the highest common factor (HCF) of 16 and 24 Answer 1 (b) Work out the lowest common multiple (LCM) of 10 and 15 Answer 1 (c) Write 42 as a product
- June 2025, Paper 3H, Q20 (3 marks): (a) Factorise fully 3n2 + 5n + 2 Answer 20 (b) A sequence has nth term 3n2 + 5n + 2 Are any of the terms in the sequence a prime number? Tick a box. Yes No Give
- November 2024, Paper 3H, Q9 (2 marks): When x is divided by 2 the remainder is 1 When x is divided by 3 the remainder is 1 When x is divided by 4 the remainder is 1 Work out two possible values of x.
- June 2024, Paper 3H, Q17 (4 marks): (a) a and b are different prime numbers. a3 × b2 = 200 Work out the value of a4 × b Answer 17 (b) c and d are different prime numbers. Circle the equation for w
- November 2023, Paper 1H, Q1 (1 mark): Work out the lowest common multiple (LCM) of 20 and 25 Answer
- November 2023, Paper 3H, Q7 (3 marks): The first two cube numbers are 1 and 8 Show that the 3rd cube number can be written as the sum of three different prime numbers. = + +
- June 2023, Paper 1H, Q5 (3 marks): Two prime numbers are multiplied together. The answer is an even number between 50 and 60 Complete the calculation. × =
- June 2023, Paper 1H, Q7 (3 marks): 2a × 3 × 52 = 600 Work out the value of a. You must show your working. a =
- November 2022, Paper 2H, Q5 (2 marks): Written as the product of prime factors, 12 600 = 23 × 32 × 52 × 7 and 14 112 = 25 × 32 × 72 Work out the highest common factor (HCF) of 12 600 and 14 112 Give
- June 2022, Paper 2H, Q6 (2 marks): Show that 2125 can be written as a cube number multiplied by a prime number between 10 and 20
- June 2022, Paper 3H, Q26 (4 marks): Q and R are two numbers. As a product of prime factors, Q = 23 × 3 × a3 R = 24 × 32 × a2 26 (a) The highest common factor (HCF) of Q and R is 4056 Work out the
- November 2021, Paper 1H, Q5 (3 marks): Write 200 as a product of prime factors. Give your answer in index form. Answer
- November 2021, Paper 2H, Q22 (4 marks): Liam is trying to remember a 3-digit code. He knows the rule that the first digit is a cube number the second digit is a factor of 16 the third digit is an odd
- November 2021, Paper 3H, Q11 (3 marks): Erik thinks of a prime number between 20 and 30 His number is x% of 125 Work out one possible value of x. Answer
- November 2020, Paper 1H, Q14 (4 marks): (a) c = 210 × 3 × 56 Work out 18c. Give your answer as a product of prime factors in index form. Answer 14 (b) Work out 7 3 3 2 11 2 × Give your answer as an in
- November 2020, Paper 2H, Q6 (2 marks): Work out the highest common factor (HCF) of 75 and 105 Answer
- November 2019, Paper 2H, Q5 (2 marks): Work out the lowest common multiple (LCM) of 120 and 144 Answer
- June 2019, Paper 3H, Q3 (1 mark): Circle the lowest common multiple (LCM) of 5, 15 and 25 5 45 75 150
- November 2018, Paper 2H, Q17 (1 mark): a is a prime number. b is an even number. N = a2 + ab Circle the correct statement about N. could be even or odd always even always prime always odd
- November 2018, Paper 3H, Q4 (1 mark): Work out the lowest common multiple (LCM) of 20, 30 and 40 Circle your answer. 10 120 240 24 000
- November 2018, Paper 3H, Q7 (3 marks): k = n2 + 9n + 1 Mo says, “k will be a prime number for all integer values of n from 1 to 9” Show that Mo is wrong. You must show that your value of k is not pri
- June 2018, Paper 3H, Q5 (4 marks): a is a common factor of 72 and 120 b is a common multiple of 6 and 9 Work out the highest possible value of a b Answer
- June 2018, Paper 3H, Q10 (3 marks): The nth term of a sequence is 12n – 5 Work out the numbers in the sequence that have two digits and are not prime. Answer
- November 2017, Paper 3H, Q15 (1 mark): Circle the highest common factor (HCF) of 6xy2 and 4x3y 2xy2 2xy 12x3y2 24x4y3
- November 2017, Paper 3H, Q21 (3 marks): N is a number. As a product of prime factors in index form N = 2 × 34 × y3 Work out 3N 2 as a product of prime factors in index form. Give your answer in terms
- June 2017, Paper 1H, Q5 (3 marks): Write 36 as a product of prime factors. Give your answer in index form. Answer
- June 2017, Paper 2H, Q13 (4 marks): To make one cheese sandwich, Gina uses one bread roll and two cheese slices. She is going to buy enough packs to have exactly twice as many cheese slices as bre
- Specimen, Paper 2H, Q9 (3 marks): Written as the product of its prime factors 672 = 25 3 7 9 (a) Write 252 as the product of its prime factors. Answer 9 (b) Work out the value of the highest
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