Question

If $N=\mathrm{1223334444.......}$ and is a $100$-digit number, find the remainder when $N$ is divided by $16$.

• A. $15$
• B. $13$
• C. $11$
• D. $9$

Answer 1

The correct option is B $13$

See each digit is coming the number of times his value. So from $1$ to $9$ we have $45$ digits. Then $10$ times $10,11$ times $11,12$ times $12,13$ times $13.$

So, last $4$ digit will be $4141$

Now for divisibility by $16$ last $4$ digit must be checked.

Since dividing $4141$ with $16$, we get the remainder as $13$

Hence, the remainder is $13$ when $N$ is divided by $16$.