[Number Theory]
Problem: Compute the largest prime divisor of $15 !-13$ !.

Solution: Factor 15 ! -13 ! to obtain $13 !(15 \cdot 14-1)=13$ ! $\cdot 209$. The largest prime divisor of 13 ! is 13 , so continue by factoring $209=11 \cdot 19$. Thus the largest prime divisor of 15 ! - 13 ! is 19 .

Final answer: 19