Primary 4 Mathematics Factors Multiples Quiz

Primary 4 Mathematics Quiz - Factors Multiples (Answer Key)

Total Marks: 20

Section A: Multiple Choice Questions (Questions 1 to 5)

Each question carries 1 mark.

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 ÷ 5 = 7 R1, 36 ÷ 7 = 5 R1, 36 ÷ 10 = 3 R6, so 5, 7, and 10 are not factors.
• Marking: 1 mark for correct answer.

2. B) 24

• Explanation: A multiple of a number is the product of that number and a whole number. 8 × 3 = 24, so 24 is a multiple of 8. 18, 34, and 42 are not in the 8 times table (8, 16, 24, 32, 40, ...).
• Marking: 1 mark for correct answer.

3. B) 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.

4. A) 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 correct answer.

5. C) 12

• Explanation: The first common multiple is the smallest number that is a multiple of both 3 and 4. Multiples of 3: 3, 6, 9, 12, 15, ... Multiples of 4: 4, 8, 12, 16, ... The first common multiple is 12.
• Marking: 1 mark for correct answer.

Section B: Short Answer Questions (Questions 6 to 15)

Each question carries 1 mark.

6. 1, 2, 4, 7, 14, 28

• Explanation: Factors of 28 are numbers that divide 28 exactly. Check systematically: 28 ÷ 1 = 28, 28 ÷ 2 = 14, 28 ÷ 4 = 7, 28 ÷ 7 = 4, 28 ÷ 14 = 2, 28 ÷ 28 = 1. So the factors are 1, 2, 4, 7, 14, 28.
• Common mistake: Forgetting 1 and 28.
• Marking: 1 mark for all factors listed correctly.

7. Yes, because 42 ÷ 7 = 6 with no remainder.

• Explanation: A number is a factor of another if it divides it exactly. 7 × 6 = 42, so 7 divides 42 exactly. Therefore, 7 is a factor of 42.
• Marking: 1 mark for correct answer with explanation.

8. 9, 18, 27

• Explanation: Multiples of 9 are found by multiplying 9 by whole numbers: 9 × 1 = 9, 9 × 2 = 18, 9 × 3 = 27.
• Marking: 1 mark for all three multiples listed correctly.

9. 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 all common factors listed correctly.

10. 30

• Explanation: The 5th multiple of 6 is 6 × 5 = 30. The first five multiples are 6, 12, 18, 24, 30.
• Marking: 1 mark for correct answer.

11. 15, 30, 45

• Explanation: Multiples of 5 end in 0 or 5. Check each number: 15 (ends in 5 ✓), 22 (ends in 2 ✗), 30 (ends in 0 ✓), 37 (ends in 7 ✗), 45 (ends in 5 ✓), 51 (ends in 1 ✗).
• Marking: 1 mark for all three numbers circled correctly.

12. Yes, because 54 ÷ 9 = 6 with no remainder.

• Explanation: A number is a multiple of another if it can be divided exactly. 9 × 6 = 54, so 54 is a multiple of 9.
• Marking: 1 mark for correct answer with working shown.

13. 6, 12, 18

• Explanation: Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20... Multiples of 3: 3, 6, 9, 12, 15, 18, 21... Common multiples less than 20: 6, 12, 18.
• Marking: 1 mark for all three numbers listed correctly.

14. 5, 10, 20, or 40

• Explanation: Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40. Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, ... Numbers that are both factors of 40 and multiples of 5: 5, 10, 20, 40. Accept any one of these.
• Marking: 1 mark for any correct number.

15. Any pair where both numbers have 4 as a factor, e.g., 8 and 12, 4 and 16, 12 and 20.

• Explanation: Both numbers must be divisible by 4. For example, 8 ÷ 4 = 2 and 12 ÷ 4 = 3, so 4 is a common factor of 8 and 12.
• Marking: 1 mark for a correct pair.

Section C: Problem Sums (Questions 16 to 20)

Each question carries 2 marks.

16. 6 or 12

• Explanation: Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Common factors of 24 and 36: 1, 2, 3, 4, 6, 12. The possible numbers of apples per bag from the list given are 2, 3, 4, 6, 8, or 12. The common factors that are also possible numbers per bag are 6 and 12. Accept either 6 or 12.
• Marking: 1 mark for identifying common factors, 1 mark for correct final answer.

17. 7, 14, 21, 42

• Explanation: Multiples of 7: 7, 14, 21, 28, 35, 42, 49, ... Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. Numbers that are both multiples of 7 and factors of 42: 7, 14, 21, 42.
• Marking: 1 mark for listing all possible numbers, 1 mark for completeness.

18. 12

• Explanation: This is a least common multiple (LCM) problem. Multiples of 4: 4, 8, 12, 16, 20, ... Multiples of 6: 6, 12, 18, 24, ... The first common multiple is 12. So the least number of chocolates Lily could have is 12.
• Marking: 1 mark for correct method, 1 mark for correct answer.

19. Boxes of 5, because 30 is a multiple of 5 (30 ÷ 5 = 6), but 30 is not a multiple of 6 (30 ÷ 6 = 5, but 6 × 5 = 30, so actually 30 IS a multiple of 6. Correction: Both work. 30 ÷ 5 = 6 boxes, 30 ÷ 6 = 5 boxes. Both box sizes will allow packing without leftovers.

• Explanation: 30 ÷ 5 = 6, so 5 is a factor of 30. 30 ÷ 6 = 5, so 6 is also a factor of 30. Both box sizes work. The question asks which box size will allow packing without leftovers. Both 5 and 6 work. Accept either answer with correct explanation.
• Marking: 1 mark for correct reasoning, 1 mark for correct conclusion.

20. (3, 12), (6, 9), (9, 6)

• Explanation: Factors of 18: 1, 2, 3, 6, 9, 18. Multiples of 3: 3, 6, 9, 12, 15, 18, ... Find pairs where the sum is 15:
  • 3 (factor of 18) + 12 (multiple of 3) = 15 ✓
  • 6 (factor of 18) + 9 (multiple of 3) = 15 ✓
  • 9 (factor of 18) + 6 (multiple of 3) = 15 ✓
  • 18 (factor of 18) + (-3) not possible. So the possible pairs are (3, 12), (6, 9), and (9, 6).
• Marking: 1 mark for identifying possible numbers, 1 mark for all correct pairs.

End of Answer Key