 # Divisibility Rules (1)

In this worksheet, students show their understanding of the rule for divisibility by 11. 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 is the rule to test divisibility by 11.

Rule for 11

To test a number for divisibility by 11 we must find the sums of alternative digits.  This is best illustrated using examples.

Example 1

Determine whether 17281 is divisible by 11.

Method

Underline alternate numbers to get 17226

Add up the underlined digits to get the sum of 1 + 2 + 6 = 9

Add up the non-underlined digits to get the sum of 7 + 2 = 9

If these two digit sums are equal or differ by a multiple of 11, the original number is divisible by 11.

Here they are equal so 17226 is divisible by 11.

Example 2

Determine whether 17281357 is divisible by 11.

Method

Underline alternate numbers to get 17281539

Add up the underlined digits to get the sum of 1 + 2 + 1 + 3 = 7

Add up the non-underlined digits to get the sum of 7 + 8 + 5 + 9 = 29

If these two digit sums are equal or differ by a multiple of 11, the original number is divisible by 11.

Here they differ by 29 - 7 = 22 so 17281539 is divisible by 11.

Is the following number divisible by 11?

4686

Yes

No

Is the following number divisible by 11?

4386

Yes

No

Is the following number divisible by 11?

41110

No

Yes

Is the following number divisible by 11?

42141

No

Yes

Is the following number divisible by 11?

41105

No

Yes

Is the following number divisible by 11?

400015

No

Yes

Is the following number divisible by 11?

73216

No

Yes

Is the following number divisible by 11?

12276

No

Yes

Is the following number divisible by 11?

27093

No

Yes

Is the following number divisible by 11?

27082

No

Yes

Is the following number divisible by 11?

270759

No

Yes

Is the following number divisible by 11?

2703723

No

Yes

Is the following number divisible by 11?

55555

No

Yes

Is the following number divisible by 11?

555555

No

Yes

Is the following number divisible by 11?

1111111

No

Yes

Is the following number divisible by 11?

11111111

No

Yes

Is the following number divisible by 11?

9181909

No

Yes

Is the following number divisible by 11?

918174

No

Yes

Is the following number divisible by 11?

9181744

No

Yes

Is the following number divisible by 11?

100100

No

Yes

• Question 1

Is the following number divisible by 11?

4686

Yes
• Question 2

Is the following number divisible by 11?

4386

No
• Question 3

Is the following number divisible by 11?

41110

No
• Question 4

Is the following number divisible by 11?

42141

Yes
• Question 5

Is the following number divisible by 11?

41105

No
• Question 6

Is the following number divisible by 11?

400015

Yes
• Question 7

Is the following number divisible by 11?

73216

Yes
• Question 8

Is the following number divisible by 11?

12276

Yes
• Question 9

Is the following number divisible by 11?

27093

Yes
• Question 10

Is the following number divisible by 11?

27082

Yes
• Question 11

Is the following number divisible by 11?

270759

No
• Question 12

Is the following number divisible by 11?

2703723

Yes
• Question 13

Is the following number divisible by 11?

55555

No
• Question 14

Is the following number divisible by 11?

555555

Yes
• Question 15

Is the following number divisible by 11?

1111111

No
• Question 16

Is the following number divisible by 11?

11111111

Yes
• Question 17

Is the following number divisible by 11?

9181909

Yes
• Question 18

Is the following number divisible by 11?

918174

No
• Question 19

Is the following number divisible by 11?

9181744

Yes
• Question 20

Is the following number divisible by 11?

100100

Yes
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