Fatorial Grande (BigInt)

Factorial of large n

The factorial n! is the product 1 · 2 · 3 · ... · n. By convention 0! = 1, which lines up with the gamma function Γ(1) = 1. Growth is brutal. 10! = 3.628.800, 20! ≈ 2.43·10¹⁸, and 21! already overflows a 64-bit unsigned integer (2⁶⁴ ≈ 1.84·10¹⁹). Once you pass that you have to reach for arbitrary-precision integers: JavaScript's BigInt (ES2020+), Python's native int, Java's BigInteger, or a dedicated library. To give you a sense of scale, 100! ≈ 9,33·10¹⁵⁷ runs to 158 digits. When you only want a ballpark figure, Stirling's approximation is quick: n! ≈ √(2πn) · (n/e)ⁿ. The factorial also extends to real and complex numbers via the gamma function, where Γ(n+1) = n! for non-negative integers.

Applications

Factorials show up all over the place: in combinatorics (permutations of n objects), in probability (the binomial and Poisson distributions), in the Taylor series eˣ = Σ xⁿ/n!, in RSA and other corners of number theory, and in countless counting problems across computer science.

FAQ

Why is 0! = 1? Because it's the empty product, the product when there are no factors at all. Defining it that way keeps formulas like C(n,0) = n!/(0!·n!) = 1 working without special cases, and it agrees with Γ(1) = 1.

What is the maximum n in regular JavaScript? A Number (double precision) holds up to 170!; 171! tips over into Infinity. Switch to BigInt and the only ceiling is how much memory and time you're willing to spend.

Can we compute n! for non-integer n? Yes, the gamma function handles it, since n! = Γ(n+1). To take one case, (1/2)! = √π/2 ≈ 0,8862.