Question

Using the divisibility test, determine $10000001$ is divisible by $11$ or not?

Answer 1

Checking the divisibility by $11$:

Divisibility test for $11$: A number is divisible by $11$, if the difference between the sum of the digits at even places and the sum of the digits at odd places(starting from the ones place) is divisible by $11$.

Consider the number $10000001$

Sum of the digit at odd places $=1+0+0+0=1$

Sum of the digit at even places $=0+0+0+1=1$

The difference $=1-1=0$ which is divisible by $11$.

Therefore, the number $10000001$ is divisible by $11$.