2013 AMC 12B Problem 9

What is the sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12! ?

\textbf{(A)}\ 5 \qquad \textbf{(B)}\ 7 \qquad \textbf{(C)}\ 8 \qquad \textbf{(D)}\ 10 \qquad \textbf{(E)}\ 12

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