How_To_Be_Good_At_Math

CALCULATING • CHECKING FOR DIVISIBILITY 135

Checking for divisibility

A simple calculation or an observation about a number will often tell you

whether or not it can be divided exactly (without a remainder) by a whole

number. The checks in the table below will help you with your division.

2 3 4 5 6 8 9

10

A number is

divisible by

If ... Examples

If the last digit is an even number

If the sum of all its digits is divisible by 3

If the last digit is 0 or 5

If the number is even and the sum of all its

digits is divisible by 3

If the sum of the digits is divisible by 9

If the last digit is 0

If the number formed by the last two digits

is divisible by 4

8 , 12 , 56 , 134 , 5000 are all

divisible by 2

10 , 25 , 90 , 835 , 1260 are all

divisible by 5

3426

3 + 4 + 2 + 6 = 15 (15 ÷ 3 = 5)

6831

6 + 8 + 3 + 1 = 18 (18 ÷ 9 = 2)

10 , 30 , 150 , 490 , 10 000 are all divisible

by 10

18

1 + 8 = 9 (9 ÷ 3 = 3)

732

32 ÷ 4 = 8 (we can divide 32 by 4 without

a remainder, so 732 is divisible by 4)

If the number formed by the last three

digits is divisible by 8

75 160

160 ÷ 8 = 20 (we can divide 160 by 8 without

a remainder, so 75 160 is divisible by 8)

12 If the number is divisible by 3 and 4

156

156 ÷ 3 = 52 and 156 ÷ 4 = 39 (since 156 is

divisible by 3 and 4, it’s also divisible by 12)

134-135_Dividing_with_factor_pairs.indd 135 29/02/2016 14:11