1970 AHSME Problem 23

The number 10! (10 is written in base 10), when written in the base 12 system, ends in exactly k zeroes. The value of k is

\textbf{(A) }1\qquad \textbf{(B) }2\qquad \textbf{(C) }3\qquad \textbf{(D) }4\qquad \textbf{(E) } 5

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