Divisible by 11

Divisible by 11 is discussed below.

A number is divisible by 11 if the sum of the digits in the odd places and the sum of the digits in the even places difference is a multiple of 11 or zero.

Consider the following numbers which are divisible by 11, using the test of divisibility by 11: 

(i) 154, (ii) 814, (iii) 957, (iv) 1023, (v) 1122, (vi) 1749, (vii) 53856, (viii) 592845, (ix) 5048593, (x) 98521258.

(i) 154

Sum of the digits in the even place (Red Color)  = 5 

Sum of the digits in the odd places (Black Color) = 1 + 5 = 6

Difference between the two sums = 5 - 6 = – 1

-1 is divisible by 11.

Hence, 154 is divisible by 11.

(ii) 814

Sum of the digits in the even place (Red Color)  = 1

Sum of the digits in the odd places (Black Color) = 8 + 4 = 12

Difference between the two sums = 1 - 12 = – 11

-11 is divisible by 11.

Hence, 814 is divisible by 11.

(iii) 957

Sum of the digits in the even place (Red Color)  = 5

Sum of the digits in the odd places (Black Color) = 9 + 7 = 16

Difference between the two sums = 5 - 16 = – 11

-11 is divisible by 11.

Hence, 957 is divisible by 11.

(iv) 1023

Sum of the digits in the even places (Red Color)  = 0 + 3 = 3

Sum of the digits in the odd places (Black Color) = 1 + 2 = 3

Difference between the two sums = 3 - 3 = 0

0 is divisible by 11.

Hence, 1023 is divisible by 11.

(v) 1122

Sum of the digits in the even places (Red Color)  = 1 + 2 = 3

Sum of the digits in the odd places (Black Color) = 1 + 2 = 3

Difference between the two sums = 3 - 3 = 0

0 is divisible by 11.

Hence, 1122 is divisible by 11.

(vi) 1749

Sum of the digits in the even places (Red Color)  = 7 + 9 = 16

Sum of the digits in the odd places (Black Color) = 1 + 4 = 5

Difference between the two sums = 16 - 5 = 11

11 is divisible by 11.

Hence, 1749 is divisible by 11.

(vii) 53856

Sum of the digits in the even places (Red Color)  = 3 + 5 = 8

Sum of the digits in the odd places (Black Color) = 5 + 8 + 6 = 19

Difference between the two sums = 8 - 19 = -11

-11 is divisible by 11.

Hence, 53856 is divisible by 11.

(viii) 592845

Sum of the digits in the even places (Red Color) = 9 + 8 + 5 = 22

Sum of the digits in the odd places (Black Color) = 5 + 2 + 4 = 11

Difference between the two sums = 22 - 11 = 11

11 is divisible by 11.

Hence, 592845 is divisible by 11.

(ix) 5048593

Sum of the digits in the even places (Red Color) = 0 + 8 + 9 = 17

Sum of the digits in the odd places (Black Color) = 5 + 4 + 5 + 3 = 17

Difference between the two sums = 17 - 17 = 0

0 is divisible by 11.

Hence, 5048593 is divisible by 11.

(x) 98521258

Sum of the digits in the even places (Red Color) = 8 + 2 + 2 + 8 = 20

Sum of the digits in the odd places (Black Color) = 9 + 5 + 1 + 5 = 20

Difference between the two sums = 20 - 20 = 0

0 is divisible by 11.

Hence, 98521258 is divisible by 11.

Multiplication Magic of 11:

Multiplication of 11 by 13 i.e., 13 × 11

Add the digits of that number which is multiplied by 11 i.e., in 13, 1 + 3 = 4.

Introduce this number in the middle of 13.

Now, the product of 13 × 11 will be 143, i.e., 13 × 11 = 143

To check whether a number is divisible by 11, we find the sum of the digits in the even places and the odd places separately. Now, check the difference between the two sums if it is 0 or divisible by 11, then the given number is divisible by 11.

For example:

1. Is 852346 divisible by 11?

Solution:

Sum of digits in even places (Red Color) = 5 + 3 + 6 = 14

Sum of digits in odd places (Black Color) = 8 + 2 + 4 = 14

Difference = 14 - 14 = 0

Therefore, 852346 is divisible by 11.

2. Is 85932 divisible by 11?

Solution:

Sum of digits in even places (Red Color) = 5 + 3 = 8

Sum of digits in odd places (Black Color) = 8 + 9 + 2 = 19

Difference = 8 - 19 = -11

-11 is divisible by 11.

Therefore, 85932 is divisible by 11.

3. Check whether 27896 is divisible by 11 or not.

Solution:

The sum of the digits at add places is (2 + 8 + 6) = 16.

The sum of the digits at even places is (7 + 9) = 16.

Their difference is 16 - 16 = 0, which is divisible by 11.

Therefore, the number 27896 is divisible by 11.

4. Check the divisibility of the given numbers by 11.

(i) 45982

(ii) 694201

(iii) 102742

(iv) 73953

(v) 326117

(vi) 5676

Answer: (i) 45982 is not divisible by 11.

(ii) 694201 is not divisible by 11.

(iii) 102742 is not divisible by 11.

(iv) 73953 is divisible by 11.

(v) 326117 is divisible by 11.

(vi) 5676 is divisible by 11.

● Divisibility Rules.

• Properties of Divisibility.
• Divisible by 2.
• Divisible by 3.
• Divisible by 4.
• Divisible by 5.
• Divisible by 6.
• Divisible by 7.
• Divisible by 8.
• Divisible by 9.
• Divisible by 10.
• Problems on Divisibility Rules
• Worksheet on Divisibility Rules

5th Grade Math Problems

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