  # Divisibility Rules: 4, 6, 8 and 9 (2)

In this worksheet, students use the rules for divisibility by 4, 6, 8 and 9 to find the missing digits. Key stage:  KS 3

Curriculum topic:   Number

Curriculum subtopic:   Use Concepts and Vocabulary for All Numbers

Difficulty level:   #### Worksheet Overview

Instead of actually carrying out a division, it is possible to "test" a number to see if it can be divided exactly by certain numbers.

If a number divides exactly into a number, it is divisible by this number.

24 is divisible by 2, because 24 ÷ 2 is a whole number.

24 is not divisible by 5, because 24 ÷ 5 is not a whole number.

Here are the rules to test divisibility by 4, 6, 8 and 9.

Rule for 6

Both the rules for 2 and 3 must work

A number is divisible by 2 if it ends in 0, 2, 4, 6 or 8.

This means that it is even.

A number is divisible by 3 if the sum of its digits is divisible by 3

3045 is divisible by 3, because 3 + 0 + 4 + 5 = 12 which is divisible by 3

3044 is therefore not divisible by 3, because 11 is not divisible by 3.

1044 is divisible by 6 because it is divisible by 2 and by 3.

Rule for 9

This is similar to the rule for 3.

A number is divisible by 9 if the sum of its digits is divisible by 9

7065 is divisible by 9, because 7 + 0 + 6 + 5 = 18 which is divisible by 9

3045 is therefore not divisible by 9, because 12 is not divisible by 9.

Rule for 4

A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

3140 is divisible by 4, because 40 is divisible by 4.

3145 is not divisible by 4, because 45 is not divisible by 4.

Rule for 8

A number is divisible by 8 if the number formed by its last three digits is divisible by 8.

3240 is divisible by 8, because 240 is divisible by 8.

3145 is not divisible by 8, because 145 is not divisible by 8.

Example 1

Is 3813 divisible by 6?

No, because 3 + 8 + 1 + 3 = 15, which is divisible by 3, but it is not divisible by 2 as it ends in a 3 which is odd.

Example 2

Is 2153864 divisible by 4?

Yes, because 64 is divisible by 4.

Example 3

Select all the digits which could replace ? to make the following number divisible by 4.

7085?

Think about which numbers you should pick to make 5? divisible by 4.

56 ÷ 4 = 14

52 ÷ 4 = 13

Only 6 and 2 will make the number divisible by 4.

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