Question

why is 0! = 1 ?(0 Factorial)​

Answer 1

Answer

It can be found as :

1!= 1

2!= 1*2= 2

3!= 1*2*3= 6

4!= 1*2*3*4= 24

If we change way of observing these factorial we have

3!= 4!/4 (which is 6)

2!= 3!/3(which is 2)

1!= 2!/2(which is 1)

0! = 1!/1( which is 1)

so

0! = 1

hope it helps ✌

Answer 2

First of all we need to know the Definition of factorial:-

x! = x. (x-1).(x-2).(x-3)........... 3.2.1

Example :- 5! = 5× (5-1) ×(5-2) ×(5-3) (5-4)

5! = 5×4×3×2×1

Manipulate the definition:-

x! = x × ( x-1)!

Example :- 5! = 5×(5-1)!

5! = 5× 4! = 5×4×3×2×1

Rearrange the terms:-

x! = x×(x-1)!

(x-1)! = $\frac{x\:!}{x}$

Let's find the 0!

(1-1)! = $\frac{1\:!}{1}$

0! = 1