factorial : Java Glossary

2007-10-14 by Roedy Green ©1996-2008 Canadian Mind Products
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factorial: Factorial is product of an integer and all smaller integers. It is denoted with an exclamation mark. e.g. 4! is 4 * 3 * 2 * 1 = 24.
Factorial methods are often written recursively just to show off. Iterative coding with a pedestrian for loop is much faster. Mathematicians like to use a powerful theorem proving technique called induction that works much like recursion, so they are enamoured of it and tend to recursion in Java where it is not warranted.
Recursive Calculation

Iterative Calculation

Table Lookup
Since you can’t fit n! into a long for n>20, you might as well use table lookup for a very fast factorial:

Stirling Approximation
Unfortunately, you can only calculate factorial of integers 20 or smaller, even with long arithmetic. To handle bigger ones you must use Stirling’s approximation or a Gamma function.
For hints on faster algorithms you might use to calculate large factorials see Peter’s Math Pages.
Factorials 1 to 30
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

Gamma function
Peter’s Math Pages
primes
recursion
Stirling’s approximation

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Recursive Calculation

Iterative Calculation

Table Lookup

Stirling Approximation

Factorials 1 to 30