Key observations-

• $31$ is the largest prime $< 36$. So one factorial must be atleast $31!$
• $36! = 35! \times 36 = 35! \times 3! \times 3!$
• For any factorial $31 \leq k! < 35!$, $36! \neq k!m$ where $m$ is the product of at most $3$ factorials. This can be checked by factorizing $\frac{36!}{k!}$.
• $0! = 1! = 1$