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?

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