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Factorial Calculator

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.


What is a Factorial ?

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)

Examples

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

Factorial Calculator

Oxford Dictionary Definition of Factorial

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

Factorial Table of numbers from 1 to 50 value

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 Factorial

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

FAQs

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.