Page 14 - 新思维数学活动用书7 样章

1.4 Highest common factors

Practice

5 Find the highest common factor of:
a 18 and 21 b 18 and 27 c 18 and 36

6 Find the highest common factor of:
a 27 and 45 b 50 and 75 c 40 and 72 d 24 and 35

7 Find the highest common factor of:
a 70 and 77 b 70 and 85 c 70 and 84

8 a Find the highest common factor of 32 and 40.
32
b Use your answer to part a to simplify the fraction .
40
9 a Find the highest common factor of 52 and 91.
b There are 91 rooms in a hotel. 52 rooms are reserved. What fraction of the rooms

are reserved?

Challenge
10 Two numbers have a highest common factor of 5. The two numbers add up to 35. Show that there
are three possible pairs of values for the two numbers.

11 The HCF of two numbers is 4. Both numbers are more than 4 and less than 30.
a Show that the numbers could be 8 and 12.
b Show that the numbers are not 8 and 16.

c Find all the other possible values of the two numbers.
12 The HCF of two numbers is 3. One of the numbers is 9. What are the possible values of the

other number?
13 a Find the highest common factor of:
i 9 and 10 ii 20 and 21 iii 32 and 33

b 9 and 10 are consecutive numbers. 20 and 21 are consecutive numbers.
Use part a to make a conjecture about the highest common factor of two consecutive
numbers.

c What is the lowest common multiple of two consecutive numbers?

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