Modular Arithmetic – Find the Remainder When $45!$ is Divided by $47$

Question

Find the remainder when $45!$ is divided by $47$?

My approach

I am using Wilson's theorem to solve the problem.

I reduced the expression into ($47$–$1$–$1$)!/$47!$=$(47$–$1$)/$47$!-$1$/$47!$=-$1$–$1$=-$2$

Am I right in my approach.Please correct me if I am wrong?

Please correct me how to approach towards the problem.

Answer 1

$$-1\equiv46!\equiv46\cdot45!\equiv(-1)\cdot45!\pmod{47}$$

$$\implies1\equiv45!$$