Factorial is a mathematical operation denoted by the symbol "!". It represents the product of all positive integers less than or equal to a given number. For example, the factorial of 5 (denoted as 5!) equals 5 × 4 × 3 × 2 × 1, which equals 120. Factorials are commonly used in combinatorics and probability calculations, particularly in permutations and combinations. They grow rapidly as the input number increases, making them useful in various mathematical and programming contexts. Factorials of non-negative integers are always positive integers, with 0! defined as 1 by convention. The factorial function is recursive, as the factorial of a number can be expressed in terms of the factorial of a smaller number. In programming, factorial calculations are often implemented iteratively using loops or recursively through functions. Factorials have applications in various fields, including computer science, physics, and engineering, for solving problems involving arrangements, permutations, and counting possibilities.