AMC 12 2005a Problem 8

Let $A$, $M$, and $C$ be digits with

$$(100A+10M+C)(A+M+C) = 2005.$$

What is $A$?

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