Page 21 - 新思维数学学生用书7 样章

1 Integers

1.5 Tests for divisibility

In this section you will … Key words

• learn tests of divisibility to find factors of large numbers. divisible

tests for
2, 3 and 5 are all factors of 30. divisibility
You say that ‘30 is divisible by 2’ because 30 ÷ 2 does not have a remainder.

30 is divisible by 3 and 30 is divisible by 5.
30 is not divisible by 4 because 30 ÷ 4 = 7 with remainder 2 (which can be Tip
written as 7 r 2). A whole number
87 654 is a large number. is divisible by
Is 87 654 divisible by 2? By 3? By 4? By 5? 2 when 2 is a

Here are some rules for divisibility: factor of the
• A number is divisible by 2 when the last digit is 0, 2, 4, 6 or 8. number.
87 654 is divisible by 2 because the last digit is 4.
• A number is divisible by 3 when the sum of the digits is a multiple

of 3.
8 + 7 + 6 + 5 + 4 = 30 and 30 = 10 × 3, so 87 654 is divisible by 3.
• A number is divisible by 4 when the number formed by the last two
digits is divisible by 4.
The last two digits of 87 654 are 54 and 54 ÷ 4 = 13 r 2. So 87 654 is not

divisible by 4.
• A number is divisible by 5 when the last digit is 0 or 5.
The last digit of 87 654 is 4, so it is not divisible by 5.

• A number is divisible by 6 when it is divisible by 2 and 3.
87 654 is divisible by 6.
• To test for divisibility by 7, remove the last digit, 4, to leave 8765
• Subtract twice the last digit from 8765, that is:
8765 − 2 × 4 = 8765 − 8 = 8757

• If this number is divisible by 7, so is the original number.
• 8757 ÷ 7 = 1251 with no remainder and so 87 654 is divisible

by 7.
• A number is divisible by 8 when the number formed by the last three
digits is divisible by 8.
654 ÷ 8 = 81 r 6, so 87 654 is not divisible by 8.

20