2011 AMC 8 Problem 17

#1
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?

\( \textbf{(A) } 21\qquad\textbf{(B) }25\qquad\textbf{(C) }27\qquad\textbf{(D) }35\qquad\textbf{(E) }56 \)