Primary 4 Mathematics Factors Multiples Quiz

P4 Maths Quiz: Factors & Multiples - Answer Key

Questions: 20
Time: 30 minutes
Total Marks: 40

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Section A: Multiple Choice Questions (10 marks)

1. Which of the following is a factor of 36? (2 marks)

Answer: (3) 9

Explanation: 36 ÷ 9 = 4, so 9 is a factor of 36.

• Check: 36 ÷ 8 = 4.5 (not a whole number)
• 36 ÷ 7 = 5.14... (not a whole number)
• 36 ÷ 5 = 7.2 (not a whole number)

2. How many factors does 24 have? (2 marks)

Answer: (3) 8

Explanation: The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24 Count: 1, 2, 3, 4, 5, 6, 7, 8 = 8 factors

3. Which number is a multiple of both 4 and 6? (2 marks)

Answer: (4) 24

Explanation:

• Multiples of 4: 4, 8, 12, 16, 20, 24...
• Multiples of 6: 6, 12, 18, 24...
• Common multiples: 12, 24...
• 24 ÷ 4 = 6 ✓ and 24 ÷ 6 = 4 ✓

4. What is the greatest common factor of 18 and 24? (2 marks)

Answer: (2) 6

Explanation:

• Factors of 18: 1, 2, 3, 6, 9, 18
• Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
• Common factors: 1, 2, 3, 6
• Greatest common factor: 6

5. Which of the following is a prime number? (2 marks)

Answer: (4) 29

Explanation: A prime number has exactly 2 factors (1 and itself).

• 21 = 3 × 7 (not prime)
• 25 = 5 × 5 (not prime)
• 27 = 3 × 9 (not prime)
• 29 has only factors 1 and 29 (prime)

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Section B: Short Answer Questions (15 marks)

6. List all the factors of 20. (3 marks)

Answer: 1, 2, 4, 5, 10, 20

Working: Find all numbers that divide 20 exactly:

• 20 ÷ 1 = 20 ✓
• 20 ÷ 2 = 10 ✓
• 20 ÷ 4 = 5 ✓
• 20 ÷ 5 = 4 ✓
• 20 ÷ 10 = 2 ✓
• 20 ÷ 20 = 1 ✓

7. Find the first 5 multiples of 7. (3 marks)

Answer: 7, 14, 21, 28, 35

Working:

• 7 × 1 = 7
• 7 × 2 = 14
• 7 × 3 = 21
• 7 × 4 = 28
• 7 × 5 = 35

8. Find all the common factors of 12 and 18. (3 marks)

Working:

• Factors of 12: 1, 2, 3, 4, 6, 12
• Factors of 18: 1, 2, 3, 6, 9, 18
• Common factors: 1, 2, 3, 6

Answer: 1, 2, 3, 6

9. What is the least common multiple (LCM) of 4 and 6? (3 marks)

Working:

• Multiples of 4: 4, 8, 12, 16, 20, 24...
• Multiples of 6: 6, 12, 18, 24, 30...
• Common multiples: 12, 24...
• Least common multiple: 12

Answer: 12

10. Complete the statement: (3 marks) 48 = 6 × _____, so 6 is a _______ of 48 and 48 is a _______ of 6.

 **Answer:** 48 = 6 × **8**, so 6 is a **factor** of 48 and 48 is a **multiple** of 6.

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Section C: Word Problems (15 marks)

11. Ahmad wants to arrange 40 stickers into equal rows. In how many different ways can he arrange them? List all the possible arrangements. (4 marks)

Working: Find all factor pairs of 40.

• Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
• Arrangements (rows × columns):
  • 1 row × 40 columns
  • 2 rows × 20 columns
  • 4 rows × 10 columns
  • 5 rows × 8 columns
  • 8 rows × 5 columns
  • 10 rows × 4 columns
  • 20 rows × 2 columns
  • 40 rows × 1 column

Answer: 8 different ways

Arrangements: 1×40, 2×20, 4×10, 5×8, 8×5, 10×4, 20×2, 40×1

12. Mei Ling has 24 red beads and 36 blue beads. She wants to make identical necklaces using all the beads. Each necklace must have the same number of red beads and the same number of blue beads. (5 marks)

(a) What is the greatest number of identical necklaces she can make?

Working: Find GCD of 24 and 36.

• 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: 1, 2, 3, 4, 6, 12
• Greatest common factor: 12

Answer: 12 necklaces

(b) How many red beads and blue beads will be in each necklace?

Working:

• Red beads per necklace: 24 ÷ 12 = 2
• Blue beads per necklace: 36 ÷ 12 = 3

Answer: 2 red beads and 3 blue beads in each necklace

13. Wei Ming wants to give away marbles to his friends. He can give 2, 5, or 8 marbles to each friend without having any marbles left over. What is the smallest number of marbles Wei Ming could have? (3 marks)

Working: Find LCM of 2, 5, and 8.

• Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40...
• Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40...
• Multiples of 8: 8, 16, 24, 32, 40...
• Least common multiple: 40

Answer: 40 marbles

14. A number has exactly 6 factors. Two of its factors are 3 and 4. What could the number be? Give one possible answer and explain why. (3 marks)

Working: The number must be divisible by both 3 and 4, so it must be divisible by LCM(3,4) = 12.

• Numbers that are multiples of 12: 12, 24, 36, 48...
• Check factors:
  • 12: factors are 1, 2, 3, 4, 6, 12 (6 factors) ✓
  • 24: factors are 1, 2, 3, 4, 6, 8, 12, 24 (8 factors) ✗

Answer: The number could be 12

Explanation: 12 has exactly 6 factors (1, 2, 3, 4, 6, 12), and both 3 and 4 are factors of 12.

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Total Marks: 40

Grade Boundaries:

• A: 36-40 marks (90-100%)
• B: 32-35 marks (80-89%)
• C: 28-31 marks (70-79%)
• D: 24-27 marks (60-69%)
• Below 24 marks: Needs improvement

Common Mistakes to Watch For:

1. Confusing factors with multiples
2. Missing 1 and the number itself as factors
3. Not finding the greatest/least in GCF/LCM questions
4. Calculation errors in division
5. Not listing factors in order