Factors, multiples, primes, squares and cubes – Year 5 maths test answers to download as PDF

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1. Answer to Question 1 (4 marks)

   (a) Find the factor pairs of 28: 1 × 28, 2 × 14, 4 × 7. The factors are 1, 2, 4, 7, 14, 28. (1 mark)

   (b) Count up in nines: 9, 18, 27, 36, 45. (1 mark)

   (c) Divide: 91 ÷ 7 = 13 with no remainder (7 × 13 = 91), so yes, 91 is a multiple of 7. (1 mark)

   (d) Pairs that multiply to 20: 1 × 20, 2 × 10 and 4 × 5. 3 is not a factor, so there are no other pairs. (1 mark)

2. Answer to Question 2 (4 marks)

   (a) 23, 29, 31, 37 (1 mark)

   (b) 57 = 3 × 19, so it is not prime. (1 mark)

   (c) 6² = 36; 4³ = 64. (1 mark)

   (d) 64 (8 × 8 = 64 and 4 × 4 × 4 = 64). (1 mark)

3. Answer to Question 3 (4 marks)

   (a) Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The highest common factor is 12. (1 mark)

   (b) Multiples of 6: 6, 12, 18, 24, 30. Multiples of 10: 10, 20, 30. The lowest common multiple is 30. (1 mark)

   (c) 84 = 2 × 42 = 2 × 2 × 21 = 2 × 2 × 3 × 7. (2 marks)

4. Answer to Question 4 (3 marks)

   (a) 4 + 5 + 7 + 2 = 18, which is a multiple of 9, so yes. (1 mark)

   (b) For example 120 (ends in 0 and 1 + 2 + 0 = 3). (1 mark)

   (c) A number ending in 4 is even and bigger than 2, so it has the factor 2 and is not prime. (1 mark)

5. Answer to Question 5 (5 marks)

   (a) 72 = 8 × 9 = 2 × 2 × 2 × 3 × 3 = 2³ × 3². (1 mark)

   (b) 72 ÷ 9 = 8 books. (1 mark)

   (c) The factors of 72 between 4 and 10 are 6, 8 and 9. (2 marks)

   (d) 8² = 64 and 9² = 81, so 72 is not a square number: she is wrong. (1 mark)

Total : 20 marks