Why 0!(zero factorial) = 1

We can use the pattern of series numbers to show that 0! is equal to 1.

10! = 3628800
          3628800 / 10 = 362880
9! = 362880
          362880 / 9 = 40320
8! = 40320
        40320 / 8 = 5020
7! = 5040
        5040 / 7 = 720
6!  = 720
720 / 6 = 120
5! = 120
120 / 5 = 24
4! = 24
24 / 4 = 6
3! = 6
6 / 3 = 2
2! = 2
2 / 2 = 1
1! = 1
1 / 1 = 1
0! = 1

So the relationship of the factorial numbers series is the division(if descending , like above example) or multiplication(if ascending) of the current factorial by the current number to get to the next factorial.

Do you see the pattern? That is why 0! =1.