Factorial Calculator
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About Factorials
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, 5! = 5 × 4 × 3 × 2 × 1 = 120.
Factorials are used extensively in mathematics, particularly in combinatorics, algebra, and mathematical analysis. They represent the number of ways to arrange n distinct objects into a sequence (permutations).
Our factorial calculator makes it easy to compute factorials for any non-negative integer up to 170. For values larger than 170, the result would exceed the maximum value representable in JavaScript.
Frequently Asked Questions
The factorial of a non-negative integer n is the product of all positive integers less than or equal to n. It’s denoted as n! and has important applications in permutations, combinations, and other areas of mathematics.
0! is defined as 1. This might seem counterintuitive, but it’s necessary for many mathematical formulas to work correctly, particularly in combinatorics where it represents the number of ways to arrange zero objects.
Our calculator uses JavaScript, which has a maximum number value. The factorial of 171 exceeds this limit and would be represented as “Infinity” in JavaScript. For practical purposes, factorials of numbers this large are rarely needed.
Factorials are used in permutations and combinations, probability calculations, series expansions in calculus, and many areas of algebra. They’re fundamental in combinatorics for counting problems.
Factorials grow at an extremely fast rate, faster than exponential functions. This rapid growth is why factorials of relatively small numbers can be astronomically large values.