Primary 4 Mathematics Factors Multiples Quiz

Primary 4 Mathematics Quiz - Factors Multiples: Answer Key

Total Marks: 40

Section A: Multiple Choice Questions (5 x 2 marks = 10 marks)

1. C) 9

• Explanation: A factor of a number divides the number exactly without leaving a remainder. 36 ÷ 9 = 4, so 9 is a factor of 36. 36 ÷ 7 = 5 R1, 36 ÷ 8 = 4 R4, 36 ÷ 10 = 3 R6, so 7, 8, and 10 are not factors.
• Marking: 1 mark for correct answer. 1 mark for correct working or reasoning.

2. A) 21

• Explanation: A multiple of a number is the result of multiplying that number by a whole number. 7 × 3 = 21, so 21 is a multiple of 7. 23, 25, and 27 are not multiples of 7 because they cannot be obtained by multiplying 7 by a whole number.
• Marking: 1 mark for correct answer. 1 mark for correct working or reasoning.

3. C) 6

• Explanation: A common factor is a number that divides both numbers exactly. Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. The common factors are 1, 2, 3, and 6. Among the options, only 6 is a common factor.
• Marking: 1 mark for correct answer. 1 mark for correct working or reasoning.

4. D) 5

• Explanation: Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. 24 ÷ 5 = 4 R4, so 5 is not a factor of 24. 2, 3, and 4 are all factors of 24.
• Marking: 1 mark for correct answer. 1 mark for correct working or reasoning.

5. C) 12

• Explanation: A common multiple is a number that is a multiple of both numbers. Multiples of 3: 3, 6, 9, 12, 15, 18... Multiples of 4: 4, 8, 12, 16, 20... 12 appears in both lists, so it is a common multiple of 3 and 4.
• Marking: 1 mark for correct answer. 1 mark for correct working or reasoning.

Section B: Short Answer Questions (10 x 2 marks = 20 marks)

6. 1, 3, 5, 15

• Explanation: Factors of 15 are numbers that divide 15 exactly. 15 ÷ 1 = 15, 15 ÷ 3 = 5, 15 ÷ 5 = 3, 15 ÷ 15 = 1. So the factors are 1, 3, 5, and 15.
• Marking: 1 mark for listing all factors. 1 mark for no extra numbers. Accept any order.

7. 8, 16, 24

• Explanation: The first three multiples of 8 are 8 × 1 = 8, 8 × 2 = 16, and 8 × 3 = 24.
• Marking: 1 mark for listing three correct multiples. 1 mark for them being the first three.

8. Yes, 9 is a factor of 54 because 54 ÷ 9 = 6 with no remainder.

• Explanation: A factor divides a number exactly. Since 54 ÷ 9 = 6, 9 divides 54 exactly, so it is a factor.
• Marking: 1 mark for correct answer (Yes). 1 mark for correct explanation.

9. Yes, 48 is a multiple of 6 because 6 × 8 = 48.

• Explanation: A multiple of a number is the product of that number and a whole number. Since 6 × 8 = 48, 48 is a multiple of 6.
• Marking: 1 mark for correct answer (Yes). 1 mark for correct explanation.

10. 1, 2, 4, 8

• Explanation: Factors of 16: 1, 2, 4, 8, 16. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Common factors are numbers that appear in both lists: 1, 2, 4, 8.
• Marking: 1 mark for listing common factors. 1 mark for listing all four correctly.

11. 18

• Explanation: Multiples of 6: 6, 12, 18, 24... Multiples of 9: 9, 18, 27... The first common multiple is 18.
• Marking: 1 mark for correct answer. 1 mark for correct working.

12. 14

• Explanation: Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56. Common factors: 1, 2, 7, 14. The largest common factor is 14.
• Marking: 1 mark for correct answer. 1 mark for correct working.

13. 40

• Explanation: Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45... Multiples of 8: 8, 16, 24, 32, 40, 48... The smallest common multiple is 40.
• Marking: 1 mark for correct answer. 1 mark for correct working.

14. Any pair of numbers that have 4 as a common factor, e.g., 8 and 12.

• Explanation: 4 is a factor of 8 (8 ÷ 4 = 2) and 4 is a factor of 12 (12 ÷ 4 = 3), so 4 is a common factor of 8 and 12. Other acceptable answers: (4, 8), (4, 12), (8, 16), (12, 20), etc.
• Marking: 1 mark for correct pair. 1 mark for correct reasoning.

15. Any pair of numbers that have 24 as a common multiple, e.g., 3 and 8.

• Explanation: 24 is a multiple of 3 (3 × 8 = 24) and 24 is a multiple of 8 (8 × 3 = 24), so 24 is a common multiple of 3 and 8. Other acceptable answers: (2, 12), (4, 6), (3, 4), etc.
• Marking: 1 mark for correct pair. 1 mark for correct reasoning.

Section C: Problem Sums (5 x 2 marks = 10 marks)

16. 1, 2, 3, 5, 6, 10, 15, 30

• Explanation: Factors of 30 are numbers that divide 30 exactly. 30 ÷ 1 = 30, 30 ÷ 2 = 15, 30 ÷ 3 = 10, 30 ÷ 5 = 6, 30 ÷ 6 = 5, 30 ÷ 10 = 3, 30 ÷ 15 = 2, 30 ÷ 30 = 1. So the factors are 1, 2, 3, 5, 6, 10, 15, and 30.
• Marking: 1 mark for listing all factors. 1 mark for no extra numbers.

17. 12 or 24

• Explanation: Multiples of 4: 4, 8, 12, 16, 20, 24, 28... Multiples of 6: 6, 12, 18, 24, 30... Common multiples less than 30: 12 and 24. Either answer is acceptable.
• Marking: 1 mark for identifying common multiples. 1 mark for correct answer(s).

18. 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

• Explanation: Factors of 48 are numbers that divide 48 exactly. 48 ÷ 1 = 48, 48 ÷ 2 = 24, 48 ÷ 3 = 16, 48 ÷ 4 = 12, 48 ÷ 6 = 8, 48 ÷ 8 = 6, 48 ÷ 12 = 4, 48 ÷ 16 = 3, 48 ÷ 24 = 2, 48 ÷ 48 = 1. So the factors are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
• Marking: 1 mark for listing all factors. 1 mark for no extra numbers.

19. 12 necklaces

• Explanation: The greatest number of necklaces she can make is the greatest common factor of 36 and 48. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Common factors: 1, 2, 3, 4, 6, 12. The greatest common factor is 12. So she can make 12 necklaces, each with 3 red beads (36 ÷ 12 = 3) and 4 blue beads (48 ÷ 12 = 4).
• Marking: 1 mark for correct method (finding GCF). 1 mark for correct answer with units.

20. 24 seconds

• Explanation: The time when both bells ring together again is the least common multiple of 6 and 8. Multiples of 6: 6, 12, 18, 24, 30... Multiples of 8: 8, 16, 24, 32... The first common multiple is 24. So they will ring together again after 24 seconds.
• Marking: 1 mark for correct method (finding LCM). 1 mark for correct answer with units.

End of Answer Key