Breaking Down the Factorial
Factorial: It's Not Just For Integers
Let n be a positive number, where n > 0. n! can be rewritten as:
n!
= n * (n - 1)!
= n * (n - 1) * (n - 2)!
= n * (n - 1) * (n - 2) * (n - 3)!
...
= n * (n - 1) * (n - 2) * (n - 3) * ... * k
where 0 ≤ k ≤ 1. Note that 0! = 1. Keep the loop multiplying n, n - 1, n - 2, n - 3, etc. until you a multiplying a number between 0! and 1! to the total.
For certain k:
0.25! ≈ 0.9064024771
0.50! = ≈ 0.8862269255
0.75! ≈ 0.9190625268
1! = 1
Examples
3! = 3 * 2 * 1! = 3 * 2 * 1 = 6
3.25! = 3.25 * 2.25 * 1.25 * 0.25! = 9.140625 * 0.25! ≈ 8.285085142
3.5! = 3.5 * 2.5 * 1.5 * 0.5! = 13.125 * √π ÷ 2 ≈ 11.6317284
3.75! = 3.75 * 2.75 * 1.75 * 0.75! = 18.046875 * 0.75! ≈ 16.58620654
4! = 4 * 3 * 2 * 1! = 4 * 3 * 2 * 1 = 24
4.25! = 4.25 * 3.25 * 2.25 * 1.25 * 0.25! = 38.847652625 * 0.25! ≈ 35.21161185
4.5! = 4.5 * 3.5 * 2.5 * 1.5 * 0.5! = 59.0625 * √π ÷ 2 ≈ 52.3427778
4.75! = 4.75 * 3.75 * 2.75 * 1.75 * 0.75! = 85.72265625 * 0.75! ≈ 78.78448106
Factorial Values of 0 to 1
Below is a chart are the values for 0 to 1, along with several approximation polynomials. The value and polynomials have been determined using LibreOffice's Calc application.
