0! = 1 is not hard to accept, since it follows a rule. You just need to look at it backwards. To get the previous factorial (Ni-1)! you need to divide the N! by N

4! = 24 ;; 24 / 4 = 6

3! = 6 ;; 6 / 3 = 2

2! = 2 ;; 2 / 2 = 1

1!= 1 ;; 1 / 1 = 1

0! = 1