2013 AMC 10A Problem 19

In base 10, the number 2013 ends in the digit 3. In base 9, on the other hand, the same number is written as (2676)_{9} and ends in the digit 6. For how many positive integers b does the base-b-representation of 2013 end in the digit 3?

\textbf{(A)}\ 6\qquad\textbf{(B)}\ 9\qquad\textbf{(C)}\ 13\qquad\textbf{(D)}\ 16\qquad\textbf{(E)}\ 18

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.