Using divisibility tests, determine the following number is divisible by 11. The given number is 10000001?

Hint: Here in the given question a eight digit number is given and asked to check the divisibility by the given number eleven, here we need to know that the divisibility rule of eleven is that, when the number of digits are even in the given number, then add the first digit and subtract the last digit from rest of the number If the result is divisible by eleven then the whole number is divisible by eleven.


Complete step-by-step solution:
Here in the given question we know, divisibility rule of eleven, according to rule on solving we get:
The number of digits in the given number 10000001 is=8
Now according to rule we have:
\[ \Rightarrow 000000 + 1 - 1 = 0\](from rule we have to add the first digit and subtract the last digit from the rest of the number)
Now on dividing by eleven in the above obtained number we get:
\[ \Rightarrow \dfrac{0}{{11}} = 0\]
Hence the obtained number is divisible by eleven, that means the hole number is divisible by eleven.
Hence the given number 10000001 is divisible by 11.

Note: Here the given question needs to solve the division by using divisibility rule, as the given number is of eight digit hence will take time to check the divisibility, hence by using the rule we can easily check for the division of larger numbers also.