Does the integer \(k\) have a factor \(p\) such that \(1<p<k?\)

[Gmat_mission]

Does the integer \(k\) have a factor \(p\) such that \(1<p<k?\)

(1) \(k > 4!\)

(2) \(13!+2\le k \le 13!+13\)

Answer: B

Source: GMAT Prep