We know that n! = n*(n-1)*(n-2)*...........3*2*1

which means that

n! = n*(n-1)!

Dividing both sides of the equation by n, we have

(n-1)! = n!/n

Now using this fact, we can check the following pattern.

4! = 5!/5 = (5*4*3*2*1)/5 = 4*3*2*1 = 24 

3! = 4!/4 = (4*3*2*1)/4 = 3*2*1 = 6

2! = 3!/3 = (3*2*1)/3 = 2*1 = 2

1! = 2!/2 = (2*1)/2 = 1

Now, we go to 0!

0! = 1!/1 = 1/1 = 1

Hense proved.