AMC 8 2011 Problem 17

Let $w$, $x$, $y$, and $z$ be whole numbers. If $2^w \cdot 3^x \cdot 5^y \cdot 7^z = 588$, then what does $2w + 3x + 5y + 7z$ equal? $\textbf{(A) } 21 \textbf{(B) }25 \textbf{(C) }27 \textbf{(D) }35 \textbf{(E) }56$