AHSME 1970 Problem 23

The number $10!$ ($10$ is written in base $10$), when written in the base $12$ system, ends with exactly $k$ zeros. The value of $k$ is $\text{(A) } 1 \text{(B) } 2 \text{(C) } 3 \text{(D) } 4 \text{(E) } 5$