# Factorial

Well, in mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040. As you see, the factorial function (symbol: !) means to multiply a series of descending natural numbers. Another example: 4! = 4 × 3 × 2 × 1 = 24.

The value of 0! is 1, according to the convention for an empty product. Zero Factorial is really interesting, because it's generally agreed that "0! = 1". It may seem funny and it's, imho, really funny, that in this case multiplying no numbers together (nothing) results in 1, but it helps simplify a lot of equations.

So, the rule is simple, it's: n! = n × (n−1)! (which says "the factorial of any number is that number times the factorial of (that number minus 1)" That's why: 10! = 10 × 9! and 120! = 120 × 119!, etc.)

A factorial list:

n n!

0 1

1 1

2 2

3 6

4 24

5 120

6 720

7 5,040

8 40,320

9 362,880

10 3,628,800

11 39,916,800

12 479,001,600

13 6,227,020,800

14 87,178,291,200

15 1,307,674,368,000

16 20,922,789,888,000

17 355,687,428,096,000

18 6,402,373,705,728,000

19 121,645,100,408,832,000

20 2,432,902,008,176,640,000

21 51,090,942,171,709,440,000

22 1,124,000,727,777,607,680,000

23 25,852,016,738,884,976,640,000

24 620,448,401,733,239,439,360,000

25 15,511,210,043,330,985,984,000,000

It's so cool!