Question

Find the smallest and the greatest digit so that the number formed is divisible by given divisor:

Answer 1

A number is divisible by $11$ if the difference of the sum of digits at even places and sum of digits at odd places is $0$ or a multiple of $11$.

Sum of digits at odd places is $1+7=8$

Sum of digits at even places is $3+4+1=8$

Difference is $8-8=0$

So, if we write $0$ in the space then it will be the smallest digit so that the number formed is divisible by given divisor.

As, we have to write a single digit so after $0$ till $9$ there will be no other number which could be placed to have a difference of $0$ or a multiple of $11$.

Therefore, the largest digit also will be $0$