Page 11 - 新思维数学学生用书8 样章

1 Integers

Worked example 1.1

a Find the LCM of 120 and 75.
b Find the HCF of 120 and 75.

Answer

a Write 120 and 75 as products of their prime factors:
2 3 ×
120 = 2 ××× 5
2
×
753=× 55
Look at the prime factors of both numbers.
For the LCM, use the larger frequency of each prime factor.
• 120 has three 2s and 75 has no 2s. The LCM must have three 2s.
• 120 has one 3 and 75 has one 3. The LCM must have one 3.

• 120 has one 5 and 75 has two 5s. The LCM must have two 5s.
The LCM is 2 22 35 5 = 2 × 35 = 83 25 = 600
××
2
××
×××
3
×
b For the HCF use the smaller frequency of each factor: there are no 2s in 75, and there is one
3 and one 5 in both numbers.
Multiply these factors.
The HCF is 3 × 5 = 15

Exercise 1.1

Think like a mathematician

1 The factor tree for 120 in Section 1.1 started with 12 × 10.
a Draw a factor tree for 120 that starts with 6 × 20. 120
b Compare your answer to part a with a partner’s.
Are your trees the same or different?
c Draw some different factor trees for 120. Can you say 6 20

how many different trees are possible?
d Do all factor trees for 120 have the same end points?

2 a Complete this factor tree for 108. 108

b Draw a different factor tree for 108.
c Write 108 as a product of its prime factors.
d Compare your factor trees and your product of prime factors

with a partner’s. Have you drawn the same trees or different 2 54
ones? Are your trees correct?

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