Question

The remainder when 888222888222888222 . . . upto 9235 digits is divided by $5^3$ is:

• A. 103
• B. 38
• C. can't be determined
• D. none of these

Answer 1

The correct option is A 103

Since the dividend has digits repeating after every 6th digit then it can be reduced to the last four digits, which are 2228, as the rest of the digits provide a zero remainder i.e. the digits till ${9231}^{st}$ place have ${10}^{3}k$ (where k is any natural number of the form ${10}^n$) element involved which is completely divisible by $5^3$.
Hence, we have to find the remainder when 22228 is divided by $5^3$ and it is nothing but 103.