Factorial is used in permutations, combinations, probability, and series expansions.
⚠n must be a non-negative integer. Values larger than 20 may cause overflow.
What is Factorial?
The factorial function (symbol: !) says to multiply all whole numbers from our chosen number down to 1. Factorials are used in mathematics to count permutations, combinations, and in probability calculations.
Factorial of n (written n!) is the product of all positive integers up to n. n! = n × (n-1) × (n-2) × ... × 1. Used in permutations, combinations, and probability.
Why is 0! = 1?▼
0! = 1 by definition. There is exactly one way to arrange an empty set. It makes formulas like C(n,0)=1 and Taylor series work correctly.
Can factorial be calculated for negative numbers?▼
No, factorial is only defined for non-negative integers (0, 1, 2, ...). For negative numbers and fractions, use gamma function Γ(n+1) = n!.
What is the largest factorial that can be calculated?▼
In standard computing, n! grows very quickly. 12! = 479001600, 20! ≈ 2.4×10¹⁸. Beyond 20, results may exceed typical number limits.
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