Factorial Calculator is an online tool to calculate factorial of a number n!. In mathematics, the factorial of a positive number n (denoted by n! and pronounced as n factorial), is the product of all positive integers less than or

equal to n.

A factorial is a function that multiplies a number by every number less than it. Simply we can say, to find the number of way “n” objects can be arranged. For positive integer n, the product of all integers in the range 1 <=n

n! means=n (n-1) (n-2) (n-3) . . . (3) (2) (1)

0 factorial is a definition: 0! = 1. There is exactly 1 way to arrange 0 objects

2 factorial is 2! = 2 x 1 = 2. There are 2 different ways to arrange the numbers 1 through 2. {1,2} and {2,1}.

3 factorial is 3! = 3 x 2 x 1 = 6. There are 24 different ways to arrange the numbers 1 through 3. {1,2,3}, {1,3, 2}, {3, 2, 1}, {3, 1, 2}, {2, 1, 3}, {2, 3, 1}

4 factorial is 4! = 4 x 3 x 2 x 1 = 24. There are 24 different ways to arrange the numbers 1 through 4. {1,2,3,4}, {2,1,3,4}, {2,3,1,4}, {2,3,4,1}, {1,3,2,4}, etc.

5 factorial is 5! = 5 x 4 x 3 x 2 x 1 = 120

The product of an integer and all the integers below it.

By definition, the factorial of 0 is 1

For Example: Factorial of 5! is 1 . 2 . 3 . 4 . 5 = 120

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! = 355687428096000 |

18! = 6402373705728000 |

19! = 121645100408832000 |

20! = 2432902008176640000 |

21! = 51090942171709440000 |

22! = 1124000727777607680000 |

23! = 25852016738884976640000 |

24! = 620448401733239439360000 |

25! = 15511210043330985984000000 |

26! = 403291461126605635584000000 |

27! = 10888869450418352160768000000 |

28! = 304888344611713860501504000000 |

29! = 8841761993739701954543616000000 |

30! = 265252859812191058636308480000000 |

31! = 8222838654177922817725562880000000 |

32! = 263130836933693530167218012160000000 |

33! = 8683317618811886495518194401280000000 |

34! = 295232799039604140847618609643520000000 |

35! = 10333147966386144929666651337523200000000 |

36! = 371993326789901217467999448150835200000000 |

37! = 13763753091226345046315979581580902400000000 |

38! = 523022617466601111760007224100074291200000000 |

39! = 20397882081197443358640281739902897356800000000 |

40! = 815915283247897734345611269596115894272000000000 |

41! = 33452526613163807108170062053440751665152000000000 |

42! = 1405006117752879898543142606244511569936384000000000 |

43! = 60415263063373835637355132068513997507264512000000000 |

44! = 2658271574788448768043625811014615890319638528000000000 |

45! = 119622220865480194561963161495657715064383733760000000000 |

46! = 5502622159812088949850305428800254892961651752960000000000 |

47! = 258623241511168180642964355153611979969197632389120000000000 |

48! = 12413915592536072670862289047373375038521486354677760000000000 |

49! = 608281864034267560872252163321295376887552831379210240000000000 |

50! = 30414093201713378043612608166064768844377641568960512000000000000 |

Applications of factorials include combinatorics, number theory, discrete mathematics, and calculus.

Question: Can we have factorials for numbers like −1, −2, etc?

Answer: No, negative integer factorials are undefined.

Question: Can we have factorials for numbers like 0.5 or −3.217?

Answer: Yes we can. But for this you need to study Gamma Functions.

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