Factorial, superfactorial and primorial calculator online (n!, n!!, sf, #) on Intellect

is a handy online service for computing the factorial and related functions:
the double factorial, the superfactorial and the primorial. Under the hood
it uses the same high-precision calculator of the service, so the arguments can be ordinary
expressions, and the result is exact and instant on both desktop and mobile devices.


Factorial (n!). The factorial of a natural number n is the product of all natural
numbers from 1 to n:

n! = 1 · 2 · 3 · … · n, and by definition 0! = 1.

For example: 5! = 1·2·3·4·5 = 120, 10! = 3628800. The factorial counts
the number of permutations of n distinct objects and appears constantly in combinatorics,
probability theory, calculus (Taylor series) and number theory. To compute a factorial, type the
number followed by the ! sign, for example 5!.


Double factorial (n!!). This is the product of numbers of the same parity as n,
from n down to 1 or 2:

n!! = n · (n−2) · (n−4) · …

For example: 7!! = 7·5·3·1 = 105, 8!! = 8·6·4·2 = 384. To compute a
double factorial put two exclamation marks after the number: 7!!.


Superfactorial (sf). The superfactorial of n is the product of the first n
factorials:

sf(n) = 1! · 2! · 3! · … · n!

For example: sf(4) = 1!·2!·3!·4! = 1·2·6·24 = 288. The superfactorial is computed
right here with the sf function: enter sf(4) to get 288 (you can also
build it manually as 1!*2!*3!*4!). Superfactorials grow very fast and appear in
combinatorics and the theory of special functions (related to the Barnes G-function).


Primorial (n#). The primorial is the product of all prime numbers not exceeding n:

n# = 2 · 3 · 5 · 7 · 11 · … · p (all primes p ≤ n).

For example: 11# = 2·3·5·7·11 = 2310. Primorials are used in number theory, in the
search for prime numbers and to build large numbers free of small divisors. The primorial is
computed right here — put the # sign after the number, e.g. 11# gives 2310.


How to use.

1. Type an expression into the input field: 5! — factorial, 7!! — double
factorial, sf(4) — superfactorial, 11# — primorial.

2. Press the calculate button.

3. Get the exact result; it can be combined with other calculator operations:
(5! + 3!) / 2.


The service makes computing factorials fast, accurate and visual, helping students, teachers and
anyone solving combinatorics and number theory problems.