# Factorial Calculator

The factorial function is a mathematical function that operates on a non-negative integer, denoted by the symbol "!". It calculates the product of all positive integers less than or equal to the input number.$5!=\;120$120

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### The Factorial Calculator Formula

$y = n!$

### Definition of the Factorial Function

For a non-negative integer n, n factorial (denoted as n!) is the product of all positive integers from 1 to n. Mathematically, it can be expressed as:`n! = n × (n-1) × (n-2) × ... × 3 × 2 × 1`

By convention, 0 factorial (0!) is defined as 1. The factorial function is often used in various branches of mathematics, including combinatorics, probability theory, and calculus. It has applications in counting permutations, determining binomial coefficients, and solving problems related to arrangements and combinations.For example, if we calculate 5!, it would be: `5! = 5 × 4 × 3 × 2 × 1 = 120`

. Similarly, 4! is: `4! = 4 × 3 × 2 × 1 = 24`

Factorial calculations can be performed manually for small numbers, but for larger numbers, the use of calculators, programming languages, or specialized software is more practical. It's important to note that the factorial function is only defined for non-negative integers. It is not defined for non-integer numbers or negative numbers.