The factorial of n is denoted by n! and calculated by the product of integer numbers from 1 to n.

For n>0,

*n*!* = *1×2×3×4×…×*n*

For n=0,

0! = 1

### Factorial definition formula

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 = 5040

### Recursive factorial formula

*n*! = *n*×(*n*-1)!

For example:

7! = 7×(7-1)! = 7×6! = 7×720 = 5040

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### Striling’s approximation

For example:

7! ≈ √2π7 ⋅ 7^{7}⋅e^{-7 }= 5040

### Factorial table

Number n | Factorial n! |

0 | 1 |

1 | 1 |

2 | 2 |

3 | 6 |

4 | 24 |

5 | 120 |

6 | 720 |

7 | 5040 |

8 | 40320 |

9 | 362880 |

10 | 3628800 |

11 | 3.991680x10^{7} |

12 | 4.790016x10^{8} |

13 | 6.227021x10^{9} |

14 | 8.717829x10^{10} |

15 | 1.307674x10^{12} |

16 | 2.092279x10^{13} |

17 | 3.556874x10^{14} |

18 | 6.402374x10^{15} |

19 | 1.216451x10^{17} |

20 | 2.432902x10^{18} |

### C program for factorial calculation

double factorial(unsigned int n)
{ double fact=1.0; if( n > 1 ) for(unsigned int k=2; k<=n; k++) fact = fact*k; return fact; } |

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