# Factorial

The factorial operation says to multiply the designated number by every positive integer smaller than that number.

*n*! = *n* (*n* – 1) (*n* – 2) 3 2 1

When using the operation in the formulas for the number of permutations or combinations of *n* things taken *k* at a time, factorial values need to be inserted into the numerator and denominator of the fraction. The first sixteen factorial values are given here. And, by definition, 0! = 1.

n |
n! |
n |
n! |

1 | 1 | 9 | 362,880 |

2 | 2 | 10 | 3,628,800 |

3 | 6 | 11 | 39,916,800 |

4 | 24 | 12 | 479,001,600 |

5 | 120 | 13 | 6,227,020,800 |

6 | 720 | 14 | 87,178,291,200 |

7 | 5,040 | 15 | 1,307,674,368,000 |

8 | 40,320 | 16 | 20,922,789,888,000 |