Question

Using divisibility tests, determine if the given number is divisible by $11$ :

$10000001$

Answer 1

Rule for Divisibility by $11$ :

A whole number is divisible by $11$ if the difference between the sums of digits in even and odd positions is a multiple of $11$.

Here the given number is $10000001$ .

The sum of the digits at even places is $1$.
The sum of the digits at odd places is $1$.
Difference between the sum of the digits at the even and odd places $\Rightarrow 1–1=0$
The difference between the sum of the digits at odd and even places is $0$, which is a multiple of $11$.

Hence, $10000001$ is divisible by $11$.