 # Divisibility Rules: 2, 3, 5 and 10 (1)

In this worksheet, revise and practise using the rules for divisibility by 2, 3, 5 and 10. Key stage:  KS 3

Curriculum topic:   Number

Curriculum subtopic:   Use Concepts and Vocabulary for All Numbers

Difficulty level:   ### 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 2, 3, 5 and 10.

Rule for 2

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

This means that it is even.

Rule for 3

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.

Rule for 5

A number is divisible by 5 if it ends in 0 or 5.

3045 is divisible by 5, because it ends in 5.

3030 is divisible by 5, because it ends in 0.

5551 is not divisible by 5.

Rule for 10

A number is divisible by 10 if it ends in 0.

3140 is divisible by 10, because it ends in 0.

3145 is not divisible by 10.

Example

Is 3813 divisible by 3?

Yes, because 3 + 8 + 1 + 3 = 15, which is divisible by 3.

Is the following number divisible by 2?

4786

Yes

No

Is the following number divisible by 5?

4786

Yes

No

Is the following number divisible by 10?

478610

Yes

No

Is the following number divisible by 5?

478615

Yes

No

Is the following number divisible by 10?

478615

Yes

No

Is the following number divisible by 2?

478615

Yes

No

Is the following number divisible by 3?

216

Yes

No

Is the following number divisible by 3?

276

Yes

No

Is the following number divisible by 3?

27006

Yes

No

Is the following number divisible by 3?

2707

Yes

No

Is the following number divisible by 10?

27075

Yes

No

Is the following number divisible by 2?

27075

Yes

No

Is the following number divisible by 5?

27075

Yes

No

Is the following number divisible by 3?

27075

Yes

No

Is the following number divisible by 3?

13138

Yes

No

By which numbers is the following number divisible?

4104

Select each number that works.

2

3

5

10

By which numbers is the following number divisible?

7035

Select each number that works.

2

3

5

10

By which numbers is the following number divisible?

42010

Select each number that works.

2

3

5

10

By which numbers is the following number divisible?

79050

Select each number that works.

2

3

5

10

By which numbers is the following number divisible?

2287095

Select each number that works.

2

3

5

10

• Question 1

Is the following number divisible by 2?

4786

Yes
• Question 2

Is the following number divisible by 5?

4786

No
• Question 3

Is the following number divisible by 10?

478610

Yes
• Question 4

Is the following number divisible by 5?

478615

Yes
• Question 5

Is the following number divisible by 10?

478615

No
• Question 6

Is the following number divisible by 2?

478615

No
• Question 7

Is the following number divisible by 3?

216

Yes
• Question 8

Is the following number divisible by 3?

276

Yes
• Question 9

Is the following number divisible by 3?

27006

Yes
• Question 10

Is the following number divisible by 3?

2707

No
• Question 11

Is the following number divisible by 10?

27075

No
• Question 12

Is the following number divisible by 2?

27075

No
• Question 13

Is the following number divisible by 5?

27075

Yes
• Question 14

Is the following number divisible by 3?

27075

Yes
• Question 15

Is the following number divisible by 3?

13138

No
• Question 16

By which numbers is the following number divisible?

4104

Select each number that works.

2
3
• Question 17

By which numbers is the following number divisible?

7035

Select each number that works.

3
5
• Question 18

By which numbers is the following number divisible?

42010

Select each number that works.

2
5
10
• Question 19

By which numbers is the following number divisible?

79050

Select each number that works.

2
3
5
10
• Question 20

By which numbers is the following number divisible?

2287095

Select each number that works.

3
5
---- OR ----

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