Page 13 - 新思维数学学生用书8 样章

1 Integers

11 a Write each of these numbers as a product of prime numbers.
i 15 ii 15² iii 28
iv 28² v 36 vi 36²
b What do you notice about your answers to i and ii, iii and iv,
v and vi?
c If 96 = 2 × 3, show how to find the prime factors of 96 .
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Will your method work for all numbers?
12 40 = 2 × 2 × 2 × 5 and 28 = 2 × 2 × 7
Use these facts to find

a the HCF of 40 and 28 b the LCM of 40 and 28.
13 450 = 2 × 3 × 3 × 5 × 5 and 60 = 2 × 2 × 3 × 5
Use these facts to find
a the HCF of 450 and 60 b the LCM of 450 and 60.

14 180 = 2² × 3² × 5 and 54 = 2 × 3³
Use these facts to find
a the HCF of 180 and 54 b the LCM of 180 and 54.

15 a Write 45 as a product of prime numbers.
b Write 75 as a product of prime numbers.
c Find the LCM of 45 and 75.
d Find the HCF of 45 and 75.
16 a Draw factor trees to find the LCM of 90 and 140.
b Compare your answer with a partner’s. Did you draw the same

factor trees? Have you both got the same answer?
17 a Write 396 as a product of prime numbers.
b Write 168 as a product of prime numbers.

c Find the HCF of 396 and 168.
d Find the LCM of 396 and 168.
18 a Find the HCF of 34 and 58.
b Find the LCM of 34 and 58.

19 Show that the HCF of 63 and 110 is 1.
20 37 and 47 are prime numbers.
a What is the HCF of 37 and 47?
b What is the LCM of 37 and 47? Tip

c Write a rule for finding the HCF and LCM of two prime numbers. Use a calculator
d Compare your answer to part c with a partner’s answer. to help you.
Check your rules by finding the HCF and LCM of 39 and 83.

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