2002 Pascal Problem 17

The number 1000 can be written as the product of two positive integers, neither of which contains zeros. The sum of these two integers is

\textbf{(A)}\ 65\quad \textbf{(B)}\ 110\quad \textbf{(C)}\ 133\quad \textbf{(D)}\ 205\quad \textbf{(E)}\ 1001

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.