Primary 4 Mathematics · Chapter 2 · Answers and explanations
Chapter 2 Revision Paper: Factors and Multiples (answers)
Section A · Multiple choice 10 marks
1. What is the remainder when 83 is divided by 9?1 mark
(A) 9(B) 1(C) 8(D) 2
Answer: (D) 29 × 9 = 81 and 83 − 81 = 2. The remainder is 2. (The quotient, 9, is not the remainder.)
2. Hui packs 50 stickers into packets of 8. How many full packets can she make?1 mark
(A) 6(B) 7(C) 2(D) 5
Answer: (A) 68 × 6 = 48 and 8 × 7 = 56 is too many. She makes 6 full packets with 50 − 48 = 2 stickers left over.
3. Which of these is a factor of 45?1 mark
(A) 7(B) 9(C) 8(D) 10
Answer: (B) 945 ÷ 9 = 5 with no remainder, so 9 is a factor. 45 ÷ 7, 45 ÷ 8 and 45 ÷ 10 all leave a remainder.
4. Which of these is a prime number?1 mark
(A) 39(B) 51(C) 31(D) 57
Answer: (C) 3131 has only two factors, 1 and 31. Be careful: odd numbers are not always prime. 39 = 3 × 13, 51 = 3 × 17 and 57 = 3 × 19.
5. Which list shows ALL the common factors of 12 and 30?1 mark
(A) 6(B) 2, 3, 6(C) 1, 2, 3, 4, 6(D) 1, 2, 3, 6
Answer: (D) 1, 2, 3, 6Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30. The numbers in both lists are 1, 2, 3 and 6. (6 is the greatest one, but not the only one.)
6. What is the greatest common factor of 28 and 42?1 mark
(A) 14(B) 7(C) 84(D) 2
Answer: (A) 14Factors of 28: 1, 2, 4, 7, 14, 28. Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. Common factors: 1, 2, 7, 14. The greatest is 14.
7. What is the 9th multiple of 6?1 mark
(A) 15(B) 54(C) 63(D) 48
Answer: (B) 54The 9th multiple of 6 is 6 × 9 = 54. (48 is the 8th multiple and 63 is 7 × 9.)
8. Which of these is NOT a multiple of 7?1 mark
(A) 63(B) 84(C) 75(D) 91
Answer: (C) 7563 = 7 × 9, 84 = 7 × 12 and 91 = 7 × 13. But 7 × 10 = 70 and 7 × 11 = 77, so 75 is not a multiple of 7.
9. What is the smallest number that is a multiple of both 10 and 15?1 mark
(A) 5(B) 150(C) 60(D) 30
Answer: (D) 30Multiples of 10: 10, 20, 30, 40... Multiples of 15: 15, 30, 45... The first number in both lists is 30. (5 is a factor, not a multiple. 60 is also a common multiple, but it is not the smallest.)
10. Which of these is a common multiple of 4 and 6?1 mark
(A) 36(B) 18(C) 16(D) 30
Answer: (A) 3636 = 4 × 9 and 36 = 6 × 6. 18 and 30 are not multiples of 4, and 16 is not a multiple of 6.
Section B · Short answers 4 marks
11. A number divided by 7 gives a quotient of 9 and a remainder of 4. What is the number?1 mark
Answer: 67Multiply back, then add the remainder: 7 × 9 = 63, then 63 + 4 = 67.
12. List all the factors of 28.1 mark
Answer: 1, 2, 4, 7, 14, 28Look for pairs that multiply to 28: 1 × 28, 2 × 14, 4 × 7. So the factors are 1, 2, 4, 7, 14 and 28.
13. Find the greatest common factor of 24 and 40.1 mark
Answer: 8Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40. Common factors: 1, 2, 4, 8. The greatest is 8.
14. Write the first three common multiples of 6 and 9.1 mark
Answer: 18, 36, 54Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54. Multiples of 9: 9, 18, 27, 36, 45, 54. The first three numbers in both lists are 18, 36 and 54.
Section C · Show your working 16 marks
15. A baker has 94 buns. She packs 8 buns in each box. How many boxes does she need to pack ALL the buns?2 marks
Answer: 12 boxes94 ÷ 8 = 11 remainder 6. 11 boxes hold 88 buns, so 6 buns are still not packed. She needs one more box: 11 + 1 = 12 boxes.
16. Write down all the factors of 48 that are greater than 5 and smaller than 20.2 marks
Answer: 6, 8, 12, 16Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Choose those between 5 and 20: 6, 8, 12 and 16.
17. Mei has 42 apples and 63 oranges. She packs them into identical bags. All the fruit is used, and every bag has the same number of apples and the same number of oranges. What is the greatest number of bags she can pack?2 marks
Answer: 21 bagsWe need the greatest common factor of 42 and 63. Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. Factors of 63: 1, 3, 7, 9, 21, 63. Common factors: 1, 3, 7, 21. The greatest is 21, so she packs 21 bags (2 apples and 3 oranges in each).
18. The 8th multiple of a number is 96. What is the 5th multiple of the same number?2 marks
Answer: 60The number is 96 ÷ 8 = 12. The 5th multiple is 12 × 5 = 60.
19. How many multiples of 7 are there between 50 and 100?2 marks
Answer: 7List the multiples of 7: 7 × 8 = 56, 63, 70, 77, 84, 91, 98. The next one, 105, is too big. There are 7 multiples between 50 and 100.
20. Bus A leaves the interchange every 12 minutes. Bus B leaves every 15 minutes. Both buses leave together at 8:00 a.m. At what time will they next leave together?2 marks
Answer: 9:00 a.m.Find the first common multiple of 12 and 15. Multiples of 12: 12, 24, 36, 48, 60. Multiples of 15: 15, 30, 45, 60. They next leave together after 60 minutes, which is 9:00 a.m.
21. Jun has more than 80 and fewer than 100 stamps. When he puts them in rows of 6, there are 3 stamps left over. When he puts them in rows of 8, there are also 3 stamps left over. How many stamps does he have?2 marks
Answer: 99Take away the 3 left over. The number left, which is a multiple of both 6 and 8, is a common multiple of 6 and 8. The first common multiple of 6 and 8 is 24. Multiples of 24: 24, 48, 72, 96. Add 3 back: 27, 51, 75, 99. Only 99 is between 80 and 100. Check: 99 ÷ 6 = 16 remainder 3 and 99 ÷ 8 = 12 remainder 3.
22. A red light flashes every 18 seconds. A blue light flashes every 24 seconds. They flash together at the start. How many more times will they flash together in the next 5 minutes? (Do not count the flash at the start.)2 marks
Answer: 4 timesThey flash together at common multiples of 18 and 24. The first common multiple is 72 (18 × 4 and 24 × 3). So they flash together every 72 seconds: 72, 144, 216, 288. The next one, 360, is more than 5 minutes (5 × 60 = 300 seconds). So they flash together 4 more times.
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