 # Divisibility by 11

In my previous post on divisibility, I had shared the logic applied behind the divisibility check for 3 and 9. Here, I share the working behind divisibility check by 11.

### Divisibility by 11 : Method

A number is said to be divisible by 11, if the difference of sums of its alternate digits is divisible by 11.

It simply means,

Sum up the digits on odd place values and those on even place values separately => Find the difference between the sums => if the resulting value is divisible by 11, then the number is divisible by 11, as indicated below:

### Divisibility by 11 : Logic

Let’s see the logic and working behind why and how the method works!

Here, we can say:

[- a + b – c + d – e + f] is same as (b + d + f) – (a + c + e), which is nothing but the difference between sums of alternate digits, as described in the method earlier.

Through the above equation, we see that for N to be divisible by 11, the term [(b + d + f) – (a + c + e)] needs to be divisible by 11.

Let’s see few examples:

1. Nithya Veena says:

Very Interesting! Thank you for sharing the logic and refreshing the facts.. keep sharing more maths logic 😊

Liked by 1 person

1. Aswini says:

Thank you 🙂

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