Primary 4 Mathematics · Chapter 2 · Answers and explanations
Lesson 2.2: Factors (answers)
Section A · Multiple choice 4 marks
1. Which of these is a factor of 36?1 mark
(A) 8(B) 9(C) 7(D) 10
Answer: (B) 936 ÷ 9 = 4 with no remainder, so 9 is a factor. 36 ÷ 8, 36 ÷ 7 and 36 ÷ 10 all leave a remainder.
2. Which of these is a prime number?1 mark
(A) 21(B) 27(C) 29(D) 33
Answer: (C) 2929 has only two factors, 1 and 29. 21 = 3 × 7, 27 = 3 × 9 and 33 = 3 × 11, so they have more factors.
3. Which number has exactly 6 factors?1 mark
(A) 16(B) 15(C) 10(D) 12
Answer: (D) 12Factors of 12: 1, 2, 3, 4, 6, 12 (6 factors). 16 has 5 factors, 15 has 4 and 10 has 4.
4. Which of these is NOT a factor of 24?1 mark
(A) 9(B) 6(C) 8(D) 12
Answer: (A) 9Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The number 9 is not on the list because 24 ÷ 9 leaves a remainder.
Section B · Write your answer 11 marks
5. List all the factors of 20.1 mark
Answer: 1, 2, 4, 5, 10, 20Look for pairs that multiply to 20: 1 × 20, 2 × 10, 4 × 5. So the factors are 1, 2, 4, 5, 10, 20.
6. Is 51 a prime number? Give a reason.1 mark
Answer: No, 51 = 3 × 1751 ÷ 3 = 17 with no remainder, so 3 is a factor. A prime number only has the factors 1 and itself, so 51 is not prime.
7. List all the square numbers between 10 and 50.1 mark
Answer: 16, 25, 36, 494 × 4 = 16, 5 × 5 = 25, 6 × 6 = 36, 7 × 7 = 49. These are the square numbers between 10 and 50.
8. Ali arranges 24 counters in 4 rows of 6, as shown. He rearranges them into rows of 8. How many rows does he make?1 mark
Answer: 3 rows24 ÷ 8 = 3. So 8 × 3 = 24 and he makes 3 rows.
9. How many factors does 49 have?1 mark
Answer: 349 = 1 × 49 and 49 = 7 × 7. The factors are 1, 7 and 49. We write 7 only once, so there are 3 factors.
10. I am a square number between 10 and 30. I have exactly 3 factors. What number am I?2 marks
Answer: 25Square numbers between 10 and 30: 16 and 25. Factors of 16: 1, 2, 4, 8, 16 (5 factors). Factors of 25: 1, 5, 25 (3 factors). I am 25.
11. Mei arranges 36 chairs in equal rows. There is more than 1 row and each row has at least 4 chairs. List all the possible numbers of chairs in a row.2 marks
Answer: 4, 6, 9, 12, 18Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. More than 1 row means a row cannot have all 36 chairs. At least 4 chairs in a row leaves 4, 6, 9, 12, 18.
12. Ravi lists all the factors of 40. Mei lists all the factors of 45. How many more factors are in Ravi's list than Mei's?2 marks