Page 24 - 新思维数学学生用书7 样章

1.5 Tests for divisibility

10 Use the digits 4, 5, 6 and 7 to make a number that is a multiple of 11.
How many different ways can you find to do this?
11 a Show that 2521 is not divisible by any integer between 1 and 12.
b Rearrange the digits of 2251 to make a number divisible by 5.
c Rearrange the digits of 2251 to make a number divisible by 4.
d Rearrange the digits of 2251 to make a number divisible by 8.

e Find the smallest integer larger than 2521 that is divisible by 6.
f Find the smallest integer larger than 2521 that is divisible by 11.

12 44 and 44 444 are numbers where every digit is 4.
a Explain why any positive integer where every digit is 4 must be divisible by 2 and by 4.
b Here are two facts about a number:
Every digit is 4.
It is divisible by 5.
Explain why this is impossible.

c Here are two facts about a number:
Every digit is 4.
It is divisible by 3.

i Find a number with both these properties.
ii Is there more than one possible number? Give a reason for your answer.
d Here are two facts about a number:
Every digit is 4.
It is divisible by 11.

i Find a number with both these properties.
ii Is there more than one possible number? Give a reason for your answer.

Think like a mathematician

13 a 2 × 4 = 8
Look at this statement: A number is divisible by 8 when it is divisible by 2 and
by 4.

Do you think the statement is correct? Give evidence to justify your answer.
b 2 × 5 = 10
Look at this statement: A number is divisible by 10 when it is divisible by
2 and by 5.

Do you think the statement is correct? Give evidence to justify your answer.

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