Number Theory

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Divisors of $n!$

NUMTH-S4IWJU

Let $n \in \mathbb{N}$. Which of the following statements are true about the divisors of $n!$? Select ALL that apply.

A

If $m \in \mathbb{N}$ and $m \leq n$, then $m! | n!$ ($m!$ divides $n!$).

B

$n | n!$

C

$(n - 1)! | n!$

D

If $m \in \mathbb{N}$ and $m \leq n$, then $m | n!$.

E

$n^2 | n!$