Le factorial es un function que a un numero natural attribue le producto de omne numeros de 1 usque iste numero inclusive. Iste producto es representate per un puncto de exclamation postponite. Iste notation es originari del mathematico alsatian Christian Kramp (1760–1826).
Le definition es
n
!
:=
∏
i
=
1
n
i
{\displaystyle n!:=\prod _{i=1}^{n}i}
0
!
:=
1
1
!
=
1
=
1
2
!
=
1
⋅
2
=
2
3
!
=
1
⋅
2
⋅
3
=
6
4
!
=
1
⋅
2
⋅
3
⋅
4
=
24
5
!
=
1
⋅
2
⋅
3
⋅
4
⋅
5
=
120
6
!
=
1
⋅
2
⋅
3
⋅
4
⋅
5
⋅
6
=
720
7
!
=
1
⋅
2
⋅
3
⋅
4
⋅
5
⋅
6
⋅
7
=
5
,
040
8
!
=
1
⋅
2
⋅
3
⋅
4
⋅
5
⋅
6
⋅
7
⋅
8
=
40
,
320
9
!
=
1
⋅
2
⋅
3
⋅
4
⋅
5
⋅
6
⋅
7
⋅
8
⋅
9
=
362
,
880
{\displaystyle {\begin{array}{rll}0!&:=1&\\1!&=1&=1\\2!&=1\cdot 2&=2\\3!&=1\cdot 2\cdot 3&=6\\4!&=1\cdot 2\cdot 3\cdot 4&=24\\5!&=1\cdot 2\cdot 3\cdot 4\cdot 5&=120\\6!&=1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6&=720\\7!&=1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6\cdot 7&=5,040\\8!&=1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6\cdot 7\cdot 8&=40,320\\9!&=1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6\cdot 7\cdot 8\cdot 9&=362,880\end{array}}}
Le plus grande parte del calculatores electronic pote indicar maximalmente
69
!
{\displaystyle 69!}
69
!
{\displaystyle 69!}
