9. A number divided by 6 gives a quotient of 8 and a remainder of 5. What is the number?1 mark
Answer: 53Multiply back and add the remainder: 6 × 8 = 48, then 48 + 5 = 53.
10. Siti packs 75 sweets into bags of 8. How many full bags does she pack? How many sweets are left over?2 marks
Answer: 9 bags; 3 sweets left75 ÷ 8 = 9 remainder 3, because 8 × 9 = 72 and 75 − 72 = 3. She fills 9 bags and has 3 sweets left over.
11. There are 100 children going on a trip. Each minibus seats 12 children. How many minibuses are needed so that every child has a seat?2 marks
Answer: 9 minibuses100 ÷ 12 = 8 remainder 4. 8 minibuses seat 96 children, so 4 children still need a seat. We need one more minibus: 8 + 1 = 9.
12. What is the smallest number that must be added to 94 so that the answer can be divided by 7 with no remainder?2 marks
Answer: 494 ÷ 7 = 13 remainder 3. 7 × 13 = 91 and 7 × 14 = 98. 98 − 94 = 4, so we add 4.
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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
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Primary 4 Mathematics · Chapter 2 · Answers and explanations
Lesson 2.3: Common Factors (answers)
Section A · Multiple choice 4 marks
1. Which of these is a common factor of 12 and 18?1 mark
(A) 4(B) 9(C) 6(D) 36
Answer: (C) 66 × 2 = 12 and 6 × 3 = 18, so 6 is a factor of both. 4 is not a factor of 18, 9 is not a factor of 12, and 36 is a factor of neither.
2. What is the greatest common factor of 16 and 24?1 mark
(A) 4(B) 2(C) 48(D) 8
Answer: (D) 8Factors of 16: 1, 2, 4, 8, 16. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The common factors are 1, 2, 4, 8, and the greatest is 8. (48 is a common multiple, not a factor.)
3. The Venn diagram shows the factors of 18 and the factors of 24. What is the greatest common factor of 18 and 24?1 mark
(A) 6(B) 3(C) 9(D) 12
Answer: (A) 6The numbers in the middle are the common factors: 1, 2, 3, 6. The greatest of them is 6.
4. Which pair of numbers has a greatest common factor of 1?1 mark
(A) 6 and 9(B) 8 and 15(C) 10 and 15(D) 12 and 18
Answer: (B) 8 and 158 and 15 share only the factor 1. 6 and 9 share 3, 10 and 15 share 5, and 12 and 18 share 6.
Section B · Write your answer 11 marks
5. List all the common factors of 12 and 30.1 mark
Answer: 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, 6.
6. Find the greatest common factor of 36 and 48.1 mark
Answer: 12Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The greatest number in both lists is 12.
7. What is the greatest common factor of 9 and 28?1 mark
Answer: 1Factors of 9: 1, 3, 9. Factors of 28: 1, 2, 4, 7, 14, 28. Only 1 is in both lists.
8. The Venn diagram shows the factors of 20 and the factors of 30. What is the greatest common factor of 20 and 30?1 mark
Answer: 10The common factors are in the middle: 1, 2, 5, 10. The greatest is 10.
9. I am a common factor of 48 and 72. I am greater than 8 and less than 24. What number am I?1 mark
Answer: 12Common factors of 48 and 72: 1, 2, 3, 4, 6, 8, 12, 24. The only one greater than 8 and less than 24 is 12.
10. Mei has 24 pens and 36 pencils. She wants to make identical gift sets using all of them, with nothing left over. What is the greatest number of gift sets she can make?2 marks
Answer: 12 setsWe need the greatest common factor of 24 and 36. Common factors: 1, 2, 3, 4, 6, 12. The greatest is 12, so she can make 12 sets (2 pens and 3 pencils in each).
11. Ali has two ribbons, 42 cm long and 56 cm long. He cuts both into pieces of the same length with none left over. What is the greatest possible length of each piece? How many pieces does he get altogether?2 marks
Answer: 14 cm; 7 piecesGreatest common factor of 42 and 56 is 14, so each piece is 14 cm. 42 ÷ 14 = 3 pieces and 56 ÷ 14 = 4 pieces. 3 + 4 = 7 pieces.
12. A rectangular board is 48 cm long and 36 cm wide. Priya covers it completely with identical square tiles, with no gaps. What is the side of the largest possible tile? How many tiles does she use?2 marks
Answer: 12 cm; 12 tilesThe side must be a common factor of 48 and 36, and the largest is 12 cm. Along the length: 48 ÷ 12 = 4 tiles. Along the width: 36 ÷ 12 = 3 tiles. 4 × 3 = 12 tiles.
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Primary 4 Mathematics · Chapter 2 · Answers and explanations
Lesson 2.4: Multiples (answers)
Section A · Multiple choice 4 marks
1. Which of these is a multiple of 7?1 mark
(A) 58(B) 65(C) 75(D) 56
Answer: (D) 567 × 8 = 56, so 56 is a multiple of 7. Count in 7s: 7, 14, 21, 28, 35, 42, 49, 56.
2. What is the 5th multiple of 6?1 mark
(A) 30(B) 11(C) 36(D) 24
Answer: (A) 30Count in 6s five times: 6, 12, 18, 24, 30. Or 6 × 5 = 30.
3. Which of these is NOT a multiple of 9?1 mark
(A) 27(B) 56(C) 45(D) 72
Answer: (B) 569 × 3 = 27, 9 × 5 = 45 and 9 × 8 = 72. But 9 × 6 = 54 and 9 × 7 = 63, so 56 is skipped.
4. The number line shows counting in 4s. Which number does the ? stand for?1 mark
(A) 18(B) 22(C) 20(D) 24
Answer: (C) 20The jumps are +4 each time: 0, 4, 8, 12, 16, 20, 24, 28. The ? is 20.
7. Is 91 a multiple of 7? Show how you know.1 mark
Answer: Yes, 7 × 13 = 917 × 13 = 91, so 91 is a multiple of 7. (Check: 91 ÷ 7 = 13 with no remainder.)
8. The multiples of 6 are shaded on the grid. What is the next multiple of 6 after 36?1 mark
Answer: 42The shaded numbers go up by 6 each time: 6, 12, 18, 24, 30, 36. The next is 36 + 6 = 42.
9. What is the smallest multiple of 9 that is greater than 100?1 mark
Answer: 1089 × 11 = 99, which is less than 100. 9 × 12 = 108, which is greater than 100. The answer is 108.
10. I am a multiple of 6 between 40 and 60. The sum of my digits is 9. What number am I?2 marks
Answer: 54Multiples of 6 between 40 and 60: 42, 48, 54. Digit sums: 4 + 2 = 6, 4 + 8 = 12, 5 + 4 = 9. I am 54.
11. List all the multiples of 7 that are between 50 and 80.2 marks
Answer: 56, 63, 70, 777 × 7 = 49 is too small. Count on in 7s: 56, 63, 70, 77. The next is 84, which is too big.
12. Mei saves $8 every week. After how many weeks will she first have more than $100?2 marks
Answer: 13 weeks8 × 12 = 96, which is not more than $100. 8 × 13 = 104, which is more than $100. So it takes 13 weeks.
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Primary 4 Mathematics · Chapter 2 · Answers and explanations
Lesson 2.5: Common Multiples (answers)
Section A · Multiple choice 4 marks
1. Which of these is a common multiple of 4 and 6?1 mark
(A) 12(B) 8(C) 18(D) 16
Answer: (A) 1212 is in the 4 times table (4 × 3) and in the 6 times table (6 × 2). 8 and 16 are only multiples of 4. 18 is only a multiple of 6.
2. What is the first common multiple of 6 and 8?1 mark
(A) 48(B) 24(C) 14(D) 12
Answer: (B) 24Multiples of 6: 6, 12, 18, 24. Multiples of 8: 8, 16, 24. The first number in both lists is 24. (48 is a common multiple, but not the first.)
3. Some multiples of 4 and of 10 are listed. What is the first common multiple of 4 and 10?1 mark
(A) 40(B) 8(C) 20(D) 14
Answer: (C) 2020 is the first number that appears in both lists. 40 is also in both lists, but it comes later.
4. Which of these is NOT a common multiple of 4 and 6?1 mark
(A) 12(B) 24(C) 36(D) 30
Answer: (D) 3012, 24 and 36 are all in both the 4 times table and the 6 times table. 30 is a multiple of 6 but 30 ÷ 4 leaves a remainder.
Section B · Write your answer 11 marks
5. Find the first common multiple of 5 and 7.1 mark
Answer: 35Multiples of 5: 5, 10, 15, 20, 25, 30, 35. Multiples of 7: 7, 14, 21, 28, 35. The first number in both lists is 35.
6. Find the first common multiple of 9 and 12.1 mark
Answer: 36Multiples of 9: 9, 18, 27, 36. Multiples of 12: 12, 24, 36. The first number in both lists is 36.
7. Find the first common multiple of 10 and 15.1 mark
Answer: 30Multiples of 10: 10, 20, 30. Multiples of 15: 15, 30. The first number in both lists is 30.
8. Find the first common multiple of 6 and 12.1 mark
Answer: 12Multiples of 6: 6, 12. Multiples of 12: 12. The first number in both lists is 12, because 12 is itself a multiple of 6.
9. List all the common multiples of 4 and 6 that are less than 50.1 mark
Answer: 12, 24, 36, 48The first common multiple is 12. The other common multiples are multiples of 12: 12, 24, 36, 48.
10. A red bus leaves a bus stop every 6 minutes. A blue bus leaves the same stop every 8 minutes. Both buses leave together at 9:00 a.m. At what time will they next leave together?2 marks
Answer: 9:24 a.m.Find the first common multiple of 6 and 8. Multiples of 6: 6, 12, 18, 24. Multiples of 8: 8, 16, 24. It is 24, so the buses leave together again 24 minutes after 9:00 a.m., at 9:24 a.m.
11. Pencils are sold in packs of 6 and erasers in packs of 4. Ravi wants to buy the same number of pencils and erasers. What is the least number of each he can buy? How many packs of each does he buy?2 marks
Answer: 12 of each; 2 packs of pencils and 3 packs of erasersThe first common multiple of 6 and 4 is 12, so he buys 12 pencils and 12 erasers. Pencils: 12 ÷ 6 = 2 packs. Erasers: 12 ÷ 4 = 3 packs.
12. Ali visits the library every 3 days. Ben visits the library every 4 days. They both visit on a Monday. On which day of the week will they next visit on the same day?2 marks
Answer: SaturdayThe first common multiple of 3 and 4 is 12, so they meet again after 12 days. 12 days = 1 week and 5 days. 5 days after Monday is Saturday.
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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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