Question:
Determine the largest possible integer $n$ such that $942!$ is divisible by $15^n$.

Answer:
Since $15 = 3^1 \cdot 5^1$, the largest possible value of $n$ for which $15^n \mid 942!$ is the largest possible value of $n$ for which both $3^n \mid 942!$ and $5^n \mid 942!$.  Since $942!$ has many more factors of 3 than it does 5, our answer will be the number of factors of 5 in $942!$. $$ \frac{942}{5} = 188\frac{2}{5} \qquad \frac{188}{5} = 37\frac{3}{5} \qquad \frac{37}{5} = 7\frac{2}{5} \qquad \frac{7}{5} = 1\frac{2}{5} $$There are $188 + 37 + 7 + 1 = 233$ factors of 5 in $942!$, so the largest possible value of $n$ is $\boxed{233}$.