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Divisibility Rules: 4, 6, 8 and 9 (1)

In this worksheet, students use the rules for divisibility by 4, 6, 8 and 9.

'Divisibility Rules: 4, 6, 8 and 9 (1)' worksheet

Key stage:  KS 3

Curriculum topic:  Number

Curriculum subtopic:  Use Concepts and Vocabulary for All Numbers

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

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

Is 3813 divisible by 6?

 

Answer

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

Is 2153864 divisible by 4?

 

Answer

Yes, because 64 is divisible by 4.

 

Is the following number divisible by 4?

 

4786

No

Yes

Is the following number divisible by 6?

 

4386

No

Yes

Is the following number divisible by 8?

 

478640

Yes

No

Is the following number divisible by 9?

 

478611

Yes

No

Is the following number divisible by 4?

 

478615

Yes

No

Is the following number divisible by 6?

 

450015

Yes

No

Is the following number divisible by 8?

 

72216

Yes

No

Is the following number divisible by 9?

 

11276

Yes

No

Is the following number divisible by 4?

 

27006

Yes

No

Is the following number divisible by 6?

 

27072

Yes

No

Is the following number divisible by 8?

 

27075

Yes

No

Is the following number divisible by 9?

 

2703753

Yes

No

Is the following number divisible by 4?

 

27078

Yes

No

Is the following number divisible by 6?

 

270754

Yes

No

Is the following number divisible by 8?

 

18188

Yes

No

By which numbers is the following number divisible?

4104

Select each number that works.

4

6

8

9

By which numbers is the following number divisible?

1035

Select each number that works.

4

6

8

9

By which numbers is the following number divisible?

42012

Select each number that works.

4

6

8

9

By which numbers is the following number divisible?

79032

Select each number that works.

4

6

8

9

By which numbers is the following number divisible?

40044

Select each number that works.

4

6

8

9

  • Question 1

Is the following number divisible by 4?

 

4786

CORRECT ANSWER
No
  • Question 2

Is the following number divisible by 6?

 

4386

CORRECT ANSWER
Yes
  • Question 3

Is the following number divisible by 8?

 

478640

CORRECT ANSWER
Yes
  • Question 4

Is the following number divisible by 9?

 

478611

CORRECT ANSWER
Yes
  • Question 5

Is the following number divisible by 4?

 

478615

CORRECT ANSWER
No
  • Question 6

Is the following number divisible by 6?

 

450015

CORRECT ANSWER
No
  • Question 7

Is the following number divisible by 8?

 

72216

CORRECT ANSWER
Yes
  • Question 8

Is the following number divisible by 9?

 

11276

CORRECT ANSWER
No
  • Question 9

Is the following number divisible by 4?

 

27006

CORRECT ANSWER
No
  • Question 10

Is the following number divisible by 6?

 

27072

CORRECT ANSWER
Yes
  • Question 11

Is the following number divisible by 8?

 

27075

CORRECT ANSWER
No
  • Question 12

Is the following number divisible by 9?

 

2703753

CORRECT ANSWER
Yes
  • Question 13

Is the following number divisible by 4?

 

27078

CORRECT ANSWER
No
  • Question 14

Is the following number divisible by 6?

 

270754

CORRECT ANSWER
No
  • Question 15

Is the following number divisible by 8?

 

18188

CORRECT ANSWER
No
  • Question 16

By which numbers is the following number divisible?

4104

Select each number that works.

CORRECT ANSWER
4
6
8
9
  • Question 17

By which numbers is the following number divisible?

1035

Select each number that works.

CORRECT ANSWER
9
  • Question 18

By which numbers is the following number divisible?

42012

Select each number that works.

CORRECT ANSWER
4
6
9
  • Question 19

By which numbers is the following number divisible?

79032

Select each number that works.

CORRECT ANSWER
4
6
8
  • Question 20

By which numbers is the following number divisible?

40044

Select each number that works.

CORRECT ANSWER
4
6
---- OR ----

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