Divisibility Test of 11

What is meant by the divisibility test of 11?

It is the divisibility test of 11 that helps an individual to check if 11 completely divides the whole number. This particular rule states that in case the difference of the sum of the digits placed at the odd position in the given number and the sum of digits placed at the even position in the same number is 0 or 11, then the given number will be completely divisible by 11.

When performing subtraction, remember that the smaller value is deducted from the larger value. To check the number’s Divisibility by 11, the divisibility rule of 11 is the easiest and shortest method. 

It is the divisibility rule of 11 that specifies the set or condition to check if 11 can completely divide the given number without leaving any remainder.

For example, the number 363 is divisible by 11 and the remainder is 0. 

Mentioning the procedure for divisibility rule of 11:

Here mentioned are the steps following which can help you check the given number’s Divisibility by 11 through the divisibility rule of 11:

1. Start from the rightmost or leftmost digit of the given number.

2. Calculate the sum of the digits placed at the odd position in the given number.

3. Calculate the sum of the digits placed at the even position in the given number.

4. Now, subtract the smaller value from the larger value of the sum obtained in steps 2 and 3.

5. In case the difference obtained is 0 or 11 then the given number will be divisible by 11 without leaving any remainder.

Explaining the divisibility test of 11 with examples:

Now that you know the basics of the divisibility rule of 11, its time to understand the divisibility test of 11 with examples: 

1. Applying divisibility test of 11 on the number 3784: 

According to the divisibility test of 11, the difference of the sum of digits at odd places and the sum of digits at even places should be 0 or 11 for the given number 3784, to be divisible completely by 11. 

1. The sum of digits placed at an odd position in the number 3784 is 11 (3 + 8 = 11).

2. The sum of digits placed at an even position in the number 3784 is 11 (7 + 4 = 11).

3. Subtracting the smaller value from the larger value of the sum obtained in steps 1 and 2, we get 0 (11 – 11 = 0).

Now that the difference evaluated is 0, it means that the given number 3784 is completely divisible by 11.

2. Applying divisibility test of 11 on the number 53469: 

According to the divisibility test of 11, the difference between the sum of digits at odd places and the sum of digits at even places should be 0 or 11 for the given number 56419, to be divisible completely by 11. 

1. The sum of digits placed at odd position in the number 56419 is 18 (5 + 4 + 9 = 18).

2. The sum of digits placed at an even position in the number 56419 is 9 (6 + 1 = 7).

3. Subtracting the smaller value from the larger value of the sum obtained in steps 1 and 2, we get 11 (18 – 7 = 11).

Now that the difference evaluated is 11, it means that the given number 56419 is completely divisible by 11.

3. Applying divisibility test of 11 on the number 86325: 

According to the divisibility test of 11, the difference between the sum of digits at odd places and the sum of digits at even places should be 0 or 11 for the given number 86325, to be divisible completely by 11. 

1. The sum of digits placed at odd positions in the number 86325 is 11 (8 + 3 + 5 = 16).

2. The sum of digits placed at an even position in the number 86325 is 8 (6 + 2 = 8).

3. Subtracting the smaller value from the larger value of the sum obtained in steps 1 and 2, we get 8 (16 – 8 = 8).

Now that the difference evaluated is 8, it means that the given number 86325 is not completely divisible by 11.

Conclusion

The divisibility rules define the set or condition based on which an individual can check if the particular integer is divisible by another number, with the remainder as 0. It is the divisibility rules that can make it possible for the aspirants of the SSC exam to solve the division-related questions within less possible time. Therefore, it is essential for the candidates preparing for such an exam to know the basics of the same concept. Here in this article, you can learn about the divisibility test of 11 and that with the help of examples.