If N is a positive integer, is N! divisible by 14 ?

If N is a positive integer, is N! divisible by 14 ?

(1) (N+1)! is divisible by 15

(2) (N+2)! is divisible by 16


[gmatclub M22-32]

Hi Guys, is there a way to solve this algebraically? (instead of plugging in numbers as in the OE)

Thanks a ton,
A