How to prove that for any factorial of a number greater than one its result is even

Question

I'm having trouble finding a way to prove with induction that, given $n\in\mathbb{N}$ and $n>1$ then $n! = k\times2$ where $k=(n-1)*(n-2)…$.

Answer 1

The question is answered correctly in comments.

A more interesting question is to find a formula for the pattern of the powers of $2$ in $n!$

Starting with $2!$ the pattern is $$\{ 1,1,3,3,4,4,7,7,8,8,10,.....\}$$