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Factorial Calculator

Calculate factorial of numbers (n!)

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Factorial Calculator

Calculate the factorial of any number (n!). Factorials are used in permutations, combinations, probability, and many areas of mathematics.

5!
120
Factorial of 5

Calculation Steps

5! = 5 × 4 × 3 × 2 × 1 = 120

Definition: n! = n × (n-1) × (n-2) × ... × 2 × 1

Special cases: 0! = 1 and 1! = 1 by definition

Factorial Reference Table

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

Factorial Applications

Permutations

P(n,r) = n!/(n-r)!

Arrangements of objects

Combinations

C(n,r) = n!/(r!(n-r)!)

Selections of objects

Probability

Various formulas

Statistical calculations

Series Expansion

e^x = Σ(x^n/n!)

Mathematical analysis

Factorial Facts

🚀 Growth Rate

Factorials grow extremely fast! 13! is already over 6 billion, and 70! exceeds the number of atoms in the observable universe.

🎯 Real World

If you have 10 books, there are 10! = 3,628,800 different ways to arrange them on a shelf!