Tool for computing factorials. Factorial n! is the product of all integers numbers (not zero) inferior or equal to n, it is symbolized by an exclamation point juxtaposed after the number.

Factorial - dCode

Tag(s) : Arithmetics

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!

A suggestion ? a feedback ? a bug ? an idea ? *Write to dCode*!

Tool for computing factorials. Factorial n! is the product of all integers numbers (not zero) inferior or equal to n, it is symbolized by an exclamation point juxtaposed after the number.

**Factorial** of a number $ n $ is calculated with a multiplication: it is the product of the positive integers numbers (not null) less or equal to $ n $.

The usual notation to indicate a **factorial** is the exclamation mark positioned after the number. The **factorial** of $ n $ is noted $ n! $.

$$ n!=\prod_{k=1}^n k $$

__Example:__ $$ 4! = 1 \times 2 \times 3 \times 4 = 24 $$

__Example:__ The number of ways to sort a set of 52 cards is worth $ 52! = 1 \times 2 \times \dots \times 51 \times 52 = \\ 80658175170943878571660636856403766975289505440883277824000000000000 $$

Note that the **factorial** of zero is equal to one : $ 0! = 1 $

__Example:__ Here are the values of the first **factorials** $$ 0! = 1 \\ 1! = 1 \\ 2! = 2 \\ 3! = 6 \\ 4! = 24 \\ 5! = 120 \\ 6! = 720 \\ 7! = 5040 \\ 8! = 40320 \\ 9! = 362880 \\ 10! = 3628800 $$

Euler-Gamma is an extension of the **factorial** function over the complex numbers set. dCode offers calculation over the Reals. $$ \forall\,n \in \mathbb{N}, \; \Gamma(n+1)=n! $$

Use the Gamma function.

For large numbers, it is possible to estimate the value of $ n! $ with a good precision using the Stirling formula. $$ n!\sim\sqrt{2\pi n}\left(\frac{n}{e}\right)^n $$

dCode retains ownership of the online 'Factorial' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script or API access will be for free, same for Factorial download for offline use on PC, tablet, iPhone or Android !

Please, check our community Discord for help requests!

factorial,product,exclamation,mark,gamma

Source : https://www.dcode.fr/factorial

© 2020 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.

Feedback

▲