Factorials

what is the greatest prime factor of 11! + 12!

$\begin{array}{|rcll|} \hline && 11! + 12! \\ &=& 11! + 11!\cdot 12 \\ &=& 11!\cdot(1+12) \\ &=& 11! \cdot \mathbf{13} \\ \hline \end{array}$

the greatest prime factor of 11! + 12! is 13

518918400 = 2^8 * 3^4 * 5^2 * 7 * 11 * 13 - and so, it is 13.