Page 7 - 新思维数学活动用书8 样章

1 Integers

b When a square number is written as a product of prime numbers,
what can you say about the factors?
c 176 400 = 2 × 3 × 5 × 7 2
2
2
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Use this fact to show that 176 400 is a square number.
9 315 = 3 × 5 × 7 252 = 2 × 3 × 7 660 = 2 × 3 × 5 × 11
2
2
2
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Use these facts to find the highest common factor of
a 315 and 252 b 315 and 660 c 252 and 660
10 60 = 2 × 3 × 5 72 = 2 × 3 75 = 3 × 5 2
2
2
3
Use these facts to find the lowest common multiple of
a 60 and 72 b 60 and 75 c 72 and 75
11 a Write 104 as a product of its prime factors.
b Write 130 as a product of its prime factors.
c Find the HCF of 104 and 130.

d Find the LCM of 104 and 130.
12 a Write 135 as a product of prime numbers.
b Write 180 as a product of prime numbers.

c Find the HCF of 135 and 180.
d Find the LCM of 135 and 180.

Challenge
13 a Write 343 as a product of prime numbers.

b Write 546 as a product of prime numbers.
c Find the HCF of 343 and 546. d Find the LCM of 343 and 546.
14 Find the LCM of 42 and 90.

15 a Find the HCF of 168 and 264.
b Find the LCM of 168 and 264.
16 a Show that the LCM of 48 and 25 is 1.
b Find the HCF of 48 and 25.
17 The HCF of two numbers is 6. The LCM of the two numbers is 72.
What are the two numbers?

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