Page 19 - 新思维数学学生用书7 样章

1 Integers

Worked example 1.8

a Find the HCF of 16 and 40.
16
b Use your answer to part a to write the fraction as simply as possible.
40
Answer

a The factors of 16 are 1, 2, 4, 8 and 16.
The largest number in this list that is a factor of 40 is 8 (because 8 × 5 = 40).
So, the HCF of 16 and 40 is 8.
b Simplify the fraction by dividing 16 and 40 by the HCF of 16 and 40.

From part a, the HCF of 16 and 40 is 8.
So, divide both 16 and 40 by 8.
16 = 2
40 5

Exercise 1.4

1 Find the factors of:
a 24 b 50 c 45 d 19
2 Find the factors of:
a 33 b 34 c 35 d 36 e 37

3 a Find the common factors of 18 and 48.
b Find the highest common factor of 18 and 48.
4 Find the highest common factor of:
a 12 and 28 b 12 and 30 c 12 and 36

5 Find the highest common factor of:
a 18 and 24 b 19 and 25 c 20 and 26 d 21 and 28
6 Find the highest common factor of:
a 60 and 70 b 60 and 80 c 60 and 90

7 a Find the highest common factor of 35 and 56.
35
b Use your answer to part a to simplify the fraction as much as possible.
56

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