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

← Back to the worksheet

1. Answer to Question 1

   1. Factor pairs: 1 × 24, 2 × 12, 3 × 8, 4 × 6. The factors are 1, 2, 3, 4, 6, 8, 12, 24.
   2. Factor pairs: 1 × 30, 2 × 15, 3 × 10, 5 × 6. The factors are 1, 2, 3, 5, 6, 10, 15, 30.
   3. Factor pairs: 1 × 45, 3 × 15, 5 × 9. The factors are 1, 3, 5, 9, 15, 45.

2. Answer to Question 2

   1. 36: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6.
   2. 48: 1 × 48, 2 × 24, 3 × 16, 4 × 12, 6 × 8. 36 has an odd number of factors (9) because 6 × 6 uses the factor 6 only once; 48 has 10 factors.

3. Answer to Question 3

   1. 7, 14, 21, 28, 35, 42.
   2. 12, 24, 36, 48, 60, 72.
   3. 84 ÷ 7 = 12 exactly, so yes.
   4. 100 ÷ 12 = 8 remainder 4, so no.

4. Answer to Question 4

   1. 17 is prime (no factors other than 1 and 17).
   2. 21 is composite (3 × 7).
   3. 29 is prime (no factors other than 1 and 29).
   4. 51 is composite (3 × 17).
   5. 57 is composite (3 × 19).
   6. 91 is composite (7 × 13).

5. Answer to Question 5

   1. 7 × 7 = 49.
   2. 3 × 3 × 3 = 27.
   3. 12 × 12 = 144.
   4. 5 × 5 × 5 = 125.
   5. 10 × 10 × 10 = 1,000.
   6. 81 = 9 × 9, so it is a square number. It is not a cube because 4³ = 64 and 5³ = 125.

6. Answer to Question 6

   1. Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30. Common: 1, 2, 3, 6. The highest is 6.
   2. Multiples of 4: 4, 8, 12. Multiples of 6: 6, 12. The lowest common multiple is 12.
   3. 5 and 8 share no factor, so multiply: 5 × 8 = 40.

7. Answer to Question 7

   1. The factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 children per team.
   2. Between 5 and 12: 6, 9 and 12.
   3. 36 ÷ 9 = 4 teams.
   4. 38 ÷ 6 = 6 remainder 2, so no. 6 is not a factor of 38.

8. Answer to Question 8

   1. 7 × 7 = 49, so 7 tiles.
   2. 12 × 12 = 144, so 12 tiles.
   3. 144 − 49 = 95 tiles.
   4. 7² = 49 and 8² = 64. 50 is between them, so it is not a square number.

9. Answer to Question 9

   1. Every 6 minutes: 9:06, 9:12, 9:18, 9:24.
   2. Every 8 minutes: 9:08, 9:16, 9:24.
   3. The first time in both lists is 9:24 am.
   4. The lowest common multiple of 6 and 8 is 24 minutes.

10. Answer to Question 10

    1. The factor pairs of 48 give 10 ways: 1 bag of 48, 2 of 24, 3 of 16, 4 of 12, 6 of 8, and the same numbers the other way round.
    2. The sweets per bag must be 6, 8 or 12 (the factors between 5 and 15), so 8 bags of 6, 6 bags of 8 or 4 bags of 12.
    3. 60 ÷ 7 = 8 remainder 4, so no.
    4. The prime factors of 60 are 2, 3 and 5, so 2, 3 or 5 bags.

11. Answer to Question 11

    1. 2³ = 8; 3³ = 27; 4³ = 64; 5³ = 125.
    2. 64 − 27 = 37.
    3. They are cube numbers.
    4. 125 is more than 100, so no, he is 25 cubes short.

12. Answer to Question 12

    1. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
    2. There are 10 red lockers.
    3. Yes, locker 2 is the only even prime.
    4. Multiples of 6 up to 30: 6, 12, 18, 24, 30.
    5. No. Multiples of 6 are divisible by 2 and 3, so they have at least four factors and are not prime.

13. Answer to Question 13

    1. 5 × 12 = 60.
    2. Factor pairs of 60: 1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12, 6 × 10 (and the reverse).
    3. The pair 6 × 10 is the closest to a square.
    4. 64 = 8 × 8, so yes: 8 rows of 8 plants.

14. Answer to Question 14

    1. 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48.
    2. 6, 12, 18, 24, 30, 36, 42, 48.
    3. 12, 24, 36, 48.
    4. The lowest common multiple of 4 and 6 is 12, and the numbers where both happen are the multiples of 12.

15. Answer to Question 15

    1. Multiples of 12: 12, 24, 36, 48. Multiples of 18: 18, 36, 54, 72.
    2. The lowest common multiple of 12 and 18 is 36 seconds.
    3. 5 minutes is 300 seconds. 300 ÷ 36 = 8 remainder 12, so 8 times.
    4. 9 is a factor of 36, so C flashes at 36 seconds too. Yes, all three flash together every 36 seconds.
    5. 3 × 36 = 108 seconds, so 1 minute 48 seconds after midnight (00:01:48).

16. Answer to Question 16

    1. 45, 54, 63, 72.
    2. The squares near this range are 49 and 64, and neither is a multiple of 9. None of the four numbers is a square number, so all four remain: 45, 54, 63, 72.
    3. Only 72 divides by 4: 72 ÷ 4 = 18. The mystery number is 72.
    4. 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3².
    5. 144 ÷ 72 = 2 exactly, so yes, 72 is a factor of 144.

17. Answer to Question 17

    1. Pattern 5: 5² = 25. Pattern 10: 10² = 100.
    2. 25 − 16 = 9; 36 − 25 = 11.
    3. Extra tiles: 3, 5, 7, 9, 11 (from 1 to 4, 4 to 9, and so on). They are the odd numbers, going up by 2 each time.
    4. 14² = 196 and 15² = 225. The biggest is a 14 by 14 square, and 4 tiles are left over (200 − 196).
    5. 12² = 144 and 13² = 169, so 150 lies between two squares and is not possible.

18. Answer to Question 18

    1. 3 + 17 and 7 + 13.
    2. 7 + 23, 11 + 19, 13 + 17.
    3. 90 = 9 × 10 = (3 × 3) × (2 × 5), so 90 = 2 × 3 × 3 × 5 = 2 × 3² × 5.
    4. 2 × 2 × 5 × 7 = 4 × 35 = 140.
    5. 91 = 7 × 13, so it has factors 7 and 13 and is composite.

19. Answer to Question 19

    1. 3³ = 27. It is 3 × 3 × 3.
    2. A cube has 8 corners, so 8 small cubes have 3 red faces.
    3. A cube has 12 edges and each edge has 1 middle cube, so 12 cubes have 2 red faces.
    4. Each of the 6 faces has 1 centre cube, so 6 cubes have 1 red face, and the single cube in the middle has no red face (1 cube).
    5. 8 + 12 + 6 + 1 = 27. It checks.

20. Answer to Question 20

    1. Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. That is 12.
    2. Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. That is 12 as well, so the clue alone does not tell us whether the number is 60 or 72.
    3. 12: factors 1, 2, 3, 4, 6, 12 (6 factors). Check the smaller numbers: 8 has 4, 9 has 3, 10 has 4, 11 has 2. The smallest is 12.
    4. 24 has 8 factors, 36 has 9 and 48 has 10. Testing every other number below 60 in the same way shows that none has 12 factors, so the smallest is 60.