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> Let $A$ denote the set of all prime numbers, $B$ the set of all prime numbers and the number $4$, and let $C$ denote the set of positive integers $k$, for which $$\dfrac{(k-1)!}{k}$$ is *not* an integer. Then, $C=B$.
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I can see that every prime should be an element of $C$ as if $k$ is prime, then none of $1,\dots,k-1$ is divisible by $k$. Also $4$ must be there, as $1\times2\times3$ is not divisible by $4$. But I can't understand why there is no other composite number that is fatal as $4$. 

Why any composite number other that $4$ should not be element of $C$?