2015 AMC 12B Problem 23

A rectangular box measures a \times b \times c, where a, b, and c are integers and 1\leq a \leq b \leq c. The volume and the surface area of the box are numerically equal. How many ordered triples (a,b,c) are possible?

\textbf{(A)}\; 4 \qquad\textbf{(B)}\; 10 \qquad\textbf{(C)}\; 12 \qquad\textbf{(D)}\; 21 \qquad\textbf{(E)}\; 26

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