2005 Pascal Problem 15

When 14 is divided by 5, the remainder is 4. When 14 is divided by a positive integer n, the remainder is 2. For how many different values of n is this possible?

\textbf{(A)}\ 1\quad \textbf{(B)}\ 2\quad \textbf{(C)}\ 3\quad \textbf{(D)}\ 4\quad \textbf{(E)}\ 5

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.