2004 AMC 12B Problem 22

The square

\begin{array}{|c|c|c|} 50 & \textit{b} & \textit{c} \\ \textit{d} & \textit{e} & \textit{f} \\ \textit{g} & \textit{h} & 2 \\ \end{array}

is a multiplicative magic square. That is, the product of the numbers in each row, column, and diagonal is the same. If all the entries are positive integers, what is the sum of the possible values of g?

\textbf{(A)}\ 10 \qquad \textbf{(B)}\ 25 \qquad \textbf{(C)}\ 35 \qquad \textbf{(D)}\ 62 \qquad \textbf{(E)}\ 136

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.