1. [3] For what largest natural number $m$ will the number $m! \cdot 2022!$ be a factorial of a natural number?

(B. Frenkin)
Answer: when $m=2022!-1$.

Solution. (2022! - 1)!$\cdot$2022! = (2022!)!. If $m \geq 2022!$, then $m!<m!\cdot 2022!<(m+1)!$.