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.
Shukr Learns · free practice for parents and children · original questions, not affiliated with any school or agency