# how come 0! =1?

Ashwin Sinha
520 Points
11 years ago

Dear Debjit,

Usually n factorial is defined in the following way:

n! = 1*2*3*...*n

But this definition does not give a value for 0 factorial, so a natural question is: what is the value here of 0! ?

A first way to see that 0! = 1 is by working backward. We know that:

```                1! = 1
2! = 1!*2
2! = 2
3! = 2!*3
3! = 6
4! = 3!*4
4! = 24

```

We can turn this around:

```                4! = 24
3! = 4!/4
3! = 6
2! = 3!/3
2! = 2
1! = 2!/2
1! = 1
0! = 1!/1
0! = 1```

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24 Points
11 years ago

Dear Debjit,

0! = 1!/1 = 1

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jitender lakhanpal
62 Points
11 years ago

Dear DEBJIT DUTTA

WE CAN PROVE IT MATHEMATICALLY BY THE DEFINITION OF FACTORIAL

WE KNOW THAT

(N-1)! = N!/N

AND NOW PUTTING N = 1 HERE WE GET

 0! = 1!/1

AND WE KNOW

1! = 1 SO

 0! = 1

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