Divisibility condition on Sylow numbers

Statement
Suppose $$G$$ is a finite group of order:

$$N = p^km$$

where $$p$$ is prime, $$k$$ is a nonnegative integer, and $$m$$ is relatively prime to $$p$$. Let $$n_p$$ denote the $$p$$-fact about::Sylow number, i.e., the number of $$p$$-Sylow subgroups of $$G$$. Then we have:

$$n_p | m$$.

Related facts

 * Congruence condition on Sylow numbers
 * Sylow implies order-conjugate