How many values of $n<50$ exist that satisfy$ (n-1)! \ne kn$ where n,k are natural numbers? How many natural numbers less than 50 exist that satisfy $  (n-1)! \ne kn$ where n,k are natural numbers and $n \lt 50$ ?
when n=1
$0!=1*1$
when n=2
$1!\ne2*1$
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when n=49
$48!=\frac{48!}{49}*49$
Here $k = \frac{48!}{49}$ and $n =49$  

If you're only interested in the case of up to n = 49 then the answer isn't very enlightening... the answer is 16.
As the hints above suggest, you need to look at what happens when n is a prime, although you also need to take care in this case with n = 4 (can you see why?).
