Number Theory

It is 13. Because a prime number has 0 factors, it can't be any bigger. 

We factorize it first.

\(11! + 12! + 13! = 11! (1 + 12 + 12 \times 13) = 13^2 \times 11!\)

All prime factors of \(11!\) are smaller than or equal to 11 since \(11! = 11 \times 10 \times 9 \times \cdots \times 2\times 1\).

The largest prime factor is 13.