Page 20 - 新思维数学学生用书7 样章

1.4 Highest common factors

How did knowing the highest common factor help you to answer part b?

8 a Find the highest common factor of 25 and 36.
b Explain why the fraction cannot be simplified.
25
36
9 Find the highest common factor of 54, 72 and 90.
10 Two numbers have a highest common factor of 4. One of the numbers is between 10 and 20. The

other number is between 20 and 40.
a What are the two numbers? Find all the possible answers.
b How can you be sure you have all the possible answers?

Think like a mathematician

11 a Find the HCF of 8 and 12.
b Find the LCM of 8 and 12.

c Find the product of 8 and 12.
d Find the product of the HCF and the LCM of 8 and 12.
e What do you notice about the answers to parts c and d?
f Can you generalise the result in part e for different pairs of numbers?
Investigate.

12 The HCF of two numbers is 3. The LCM of the two numbers is 45.
a Explain why each number is a multiple of 3.
b Explain why each number is a factor of 45.

c Find the two numbers.
d Check with a partner to see if you have the same answers. Did you both answer the
question in the same way?

Summary checklist

I can find the highest common factor of two numbers by listing the factors of
each number.

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