Factorials

$\Huge \frac{\color{#3D99F6}{5!}}{\color{#D61F06}{6}}$ is 20. Checking the smaller ones, they doesn't work. Thus, the answer is $\boxed{5}$ .

Although $n+1$ can't be a prime factor of $n!$ , $n+1$ can share factors with $n!$ . A good way to start is to take the first two whole numbers, 2 and 3, and set their product equal to $n+1$ ; this will definitely give us a positive integer. Indeed, $\frac{5!}{6}=20;~n=\boxed{5}$