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1. Find the prime factors of the following numbers:. 120. ( i ). 120 ÷ 2 = 60. 60 ÷ 2 = 30. 30 ÷ 2 = 15. 15 ÷ 3 = 5 . 5 ÷ 5 = 1. 120 = 2 3 × 3 × 5. 1. Find the prime factors of the following numbers:. 375. (ii). 375 ÷ 3 = 125. 125 ÷ 5 = 25. 25 ÷ 5 = 5. 5 ÷ 5 = 1.

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120

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  1. 1. Find the prime factors of the following numbers: 120 (i) 120 ÷ 2 = 60 60 ÷ 2= 30 30 ÷ 2= 15 15 ÷ 3 = 5 5 ÷ 5 = 1 120 = 23 × 3 × 5

  2. 1. Find the prime factors of the following numbers: 375 (ii) 375 ÷ 3 = 125 125 ÷ 5 = 25 25 ÷ 5 = 5 5 ÷ 5 = 1 375 = 3 × 53

  3. d 1. Find the prime factors of the following numbers: 624 (iii) 624 ÷ 2 = 312 312 ÷ 2 = 156 156 ÷ 2 = 78 78 ÷ 2 = 39 39 ÷ 3 = 13 13 ÷ 13 = 1 624 = 24 × 3 × 13

  4. 1. Find the prime factors of the following numbers: 1,450 (iv) 1,450 ÷ 2 = 725 725 ÷ 5 = 145 145 ÷ 5 = 29 29 ÷ 29 = 1 1450 = 2 × 52 × 29

  5. 1. Find the prime factors of the following numbers: 24,789 (v) 24,789 ÷ 3 = 8,263 8,263 ÷ 8,263 = 1 124,789 = 3 × 8,263

  6. 2. (i) Find the prime factors of the following numbers: (a) 15,485,867 15,485,867 is prime (b) 32,452,843 32,452,843 is prime (c) 217,645,199 217,645,199 is prime (d) 694,847,539 694,847,539 is prime

  7. 2. (ii) What do the answers in (i) tell you about each of these numbers? (a) 15,485,867 They are all prime numbers; therefore they only have two factors 1 and the number itself. 15,485,867 is prime (b) 32,452,843 32,452,843 is prime (c) 217,645,199 217,645,199 is prime (d) 694,847,539 694,847,539 is prime

  8. 3. Find the highest common factor of these numbers: 18 and 30 15 and 20 (ii) (i) Factors of 15 = 3 × 5 Factors of 18 = 2 × 32 Factors of 20 = 22 × 5 Factors of 30 = 2 × 3 × 5 The onlycommon factor is 5. The commonfactors are 2 and 3. HCF = 2 × 3 = 6 HCF = 5

  9. 3. Find the highest common factor of these numbers: 16 and 24 12 and 36 (iv) (iii) Factors of 12 = 22 × 3 Factors of 16 = 24 Factors of 36 = 22 × 32 Factors of 24 = 23 × 3 The commonfactors are 22 and 3. Since 24 = 23 × 2, 23 is common to both. HCF = 23 = 8 HCF = 22 × 3 = 12

  10. 4. Jack thinks of two numbers. The HCF of these numbers is 6 and one of the numbers is 24. Suggest what his other numbers may have been. HCF = 6 = 2 × 3 Factors of 24 = 23 × 3 Two possible answers are 18 and 30: Factors of 18 = 2 × 32 Factors of 30 = 2 × 3 × 5

  11. 5. Find the HCF of each of the following: 12, 15 and 18 15, 10 and 60 (ii) (i) Factors of 15 = 3 × 5 Factors of 12 = 22 × 3 Factors of 10 = 2 × 5 Factors of 15 = 3 × 5 Factors of 60 = 22 × 3 × 5 Factors of 18 = 2 × 32 The onlycommon factor is 3. The onlycommon factor is 5. HCF = 3 HCF = 5

  12. 5. Find the HCF of each of the following: 8, 16 and 24 4, 6 and 24 (iv) (iii) Factors of 4 = 22 Factors of 8 = 23 Factors of 6 = 2 × 3 Factors of 16 = 24 Factors of 24 = 23 × 3 Factors of 24 = 23 × 3 The common factor is 23. The onlycommon factor is 2. HCF = 23 = 8 HCF = 2

  13. 6. Danielle says that the bigger a number, the more factors it has. Is she right? Use examples to justify your answer. Factors of 40 = {1, 2, 4, 5, 8, 10, 20, 40} ==> 8 factors Factors of 50 = {1, 2, 5, 10, 25, 50} ==> 6 factors Therefore, she is incorrect.

  14. 7. Find the lowest common multiple of these numbers: (i) 6 and 7 Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48 Multiples of 7 = 7, 14, 21, 28, 35, 42, 49 LCM = 42 (ii) 4 and 6 Multiples of 4 = 4, 8, 12, 16 Multiples of 6 = 6, 12, 18 LCM = 12

  15. 7. Find the lowest common multiple of these numbers: (iii) 5 and 8 Multiples of 5 = 5, 10, 15, 20, 25, 35, 40 Multiples of 8 = 8, 16, 24, 32, 40 LCM = 40 (iv) 10 and 4 Multiples of 10 = 10, 20, 30 Multiples of 4 = 4, 8, 12, 16, 20, 24 LCM = 20

  16. 7. Find the lowest common multiple of these numbers: (v) 16 and 5 Multiples of 16= 16, 32, 48, 64, 80 Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80 LCM = 80

  17. 8. The lowest common multiple of two numbers is 36. One number is 12. What might the other number be? LCM = 36 Multiples of 12 = 12, 24, 36 The number must be bigger than 12 because otherwise the LCM would be 12. Multiples of 18 = 18, 36 The othernumbercouldbe 18.

  18. 9. What is the LCM of 15 and 10 multiplied by the LCM of 6 and 20? Multiples of 15 = 15, 30 LCM = 30 Multiples of 10 = 10, 20, 30 Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 Multiples of 20 = 20, 40, 60 LCM of 15 and 10 multiplied by the LCM of 6 and 20: 30 × 60 = 1800 LCM = 60

  19. 10. What is the LCM of 18 and 12 divided by their HCF? Multiples of 18 = 18, 36 LCM = 36 Multiples of 12 = 12, 24, 36 Factors of 18 = 2 × 32 HCF = 2 × 3 = 6 Factors of 12 = 22 × 3

  20. 11. Samantha has two pieces of cloth. One piece is 72 inches wide and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How wide should she cut the strips? Factors of 72 = 23 × 32 HCF = 2 × 32 = 18 Factors of 90 = 2 × 32 × 5 Each strip should be 18 inches wide.

  21. 12. Rosa is making a game board that is 16 cm by 24 cm. She wants to use square tiles. What is the largest tile she can use? Factors of 16 = 24 HCF = 23 = 8 Factors of 24 = 23 × 3 The largest tile she can use would be 8 cm in length.

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