2003 Cayley Problem 19

The product of the digits of a four-digit number is 810. If none of the digits is repeated, the sum of the digits is

\textbf{(A)}\ 18\quad \textbf{(B)}\ 19\quad \textbf{(C)}\ 23\quad \textbf{(D)}\ 25\quad \textbf{(E)}\ 22

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 Cayley contests here.