Page 15 - 新思维数学活动用书7 样章

1 Integers

1.5 Tests for divisibility

Worked example 1.5 Key words

Use tests for divisibility to show that 3948 is divisible by 3 and 6 but divisible

not by 9. tests for
divisibility
Answer
The sum of the digits is 3 + 9 + 4 + 8 = 24.
24 is divisible by 3, so 3948 is also divisible by 3.
3948 is even and divisible by 3, so 3948 is also divisible by 6.

24 is not divisible by 9, so 3948 is also not divisible by 9.

Exercise 1.5

Focus

1 Use tests for divisibility to show that 5328 is divisible by 4 and by 9.
2 a Show that 2739 is divisible by 11.

b When the digits are reversed, the number is 9372.
Is 9372 divisible by 11? Give a reason for your answer.
3 a Show that 67 108 is divisible by 4.

b Is 67 108 divisible by 8? Give a reason for your answer.
4 The number 3812* is divisible by 3. The final digit is missing. What can you say about the
missing digit?

Practice

5 What integers less than 12 are factors of 7777?
6 a Use the digits 5, 4, 2 and 1 to make a number that is divisible by:

i 5 ii 3
b Can you arrange the digits 5, 4, 2 and 1 to make a number that is divisible by:
i 9? ii 11?

7 322 is divisible by 7. Use this fact to find a number that is divisible by 7, 2 and 3.
8 Find the smallest positive integer that is not a factor of 2520. Give reasons for your answer.

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