**Calculates the factorial of a number** positive integer with our online factorial calculator. Its operation is very simple since you only have to enter the number of which you want to calculate its factorial and press the calculate button to get the result you are looking for.

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## What is a factorial?

A **factorial of a positive integer** (n) is defined as the product of all positive integers from 1 to n. For example, let's calculate the factorial of the number 6:

6! = 6 x 5 x 4 x 3 x 2 x 1 x 1 = 720.

You may have noticed that next to the 6 there is an exclamation mark. No, we have not made a mistake. **nomenclature of a factorial** is precisely that, an exclamation mark placed to the right of the number.

## Factorial of a negative number

One of the typical classroom exercises for cheating consists of calculating the factorial of a negative number. However, by definition** it is not possible to do the factorial decomposition of negative numbers** since the function only takes into account all positive integers. This means that the factorial of a decimal number or of fractions cannot be calculated either.

## Factorial of 0

Now that we know that there are no factorials of negative numbers, which is the **factorial of 0**?

In this case, the mathematical convention established that** 0! = 1**.

If we try to justify this answer we have to resort to the following mathematical formula:

In it we can calculate the value of the previous factorial that corresponds to each positive integer n greater or equal to 1. In our case, if n=1 we have that:

(1-1)! = 0! = 1!/1 = 1

And this confirms the reason why **the factorial of zero is equal to 1**.

## Calculate factorials in Excel

In addition to using our online factorials calculator, you can also **solving factorials with Excel**. To do this, open the Microsoft program, create a new spreadsheet and in an empty cell put the following function:

=FACT()

In parentheses write the number from which you want to obtain its factorial. Remember that it must be a whole number greater than zero or else you will get an error. For example, let's calculate the** factorial of 3** in Excel:

=FACT(3)

After accepting the operation the program returns that the result is 6.

## Table of factorials

Below you will find a table that compiles the **factorials of the range of numbers from 1 to 20**. As you can see, with small numbers, we begin to handle factorials large enough that we have to resort to a calculator to figure out the result.

Number | Factorial |
---|---|

1 | 1 |

2 | 2 |

3 | 6 |

4 | 24 |

5 | 120 |

6 | 720 |

7 | 5040 |

8 | 40320 |

9 | 362880 |

10 | 3628800 |

11 | 39916800 |

12 | 479001600 |

13 | 6227020800 |

14 | 87178291200 |

15 | 1307674368000 |

16 | 20922789888000 |

17 | 3.55687428096E+14 |

18 | 6.402373705728E+15 |

19 | 1.2164510040883E+17 |

20 | 2.4329020081766E+18 |

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