Page 23 - 新思维数学学生用书7 样章

1 Integers

Exercise 1.5

1 a Show that the number 28 572 is divisible by 3 but not by 9.
b Change the final digit of 28 572 to make a number that is
divisible by 9.
2 a Show that 57 423 is divisible by 3 but not by 6.

b The number 57 42* is divisible by 6. Find the possible values of
the digit *.
3 a Show that 25 764 is divisible by 2 and by 4.
b Is 25 764 divisible by 8? Give a reason for your answer.

4 a Show that 3 and 4 are factors of 25 320.
b Find two more factors of 25 320 that are between 1 and 12.
5 a Choose any four digits.
b If it is possible, arrange your digits to make a number that is

divisible by
i 2 ii 3 iii 4 iv 5 v 6
c Can you arrange your digits to make a number that is divisible

by all five numbers in part a? If not, can you make a number
that is divisible by four of the numbers?
d Give your answers to a partner to check.
6 a Show that 924 is divisible by 11.
b Is 161 084 divisible by 11? Give a reason for your answer.

7 Use a test for divisibility test to show that:
a 2583 is divisible by 7 b 3852 is not divisible by 7
8 a Show that only two numbers between 1 and 10 are factors

of 22 599.
b What numbers between 1 and 10 are factors of 99 522?
9 Copy and complete this table. The first line has been done for you.

Number Factors between 1 and 10
12 2, 3, 4, 6
123
1234
12 345
123 456

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