Tens Digit From Remainder

Let $N$ be the unique positive integer such that dividing $273436$ by $N$
leaves a remainder of $16$ and dividing $272760$ by $N$ leaves a remainder
of $15$. What is the tens digit of $N$?

(A) $0$
(B) $1$
(C) $2$
(D) $3$
(E) $4$

Solutions