A factorial, denoted as n!, is a mathematical operation that multiplies a positive integer n by all the positive integers less than it. For example, 5! equals 5 × 4 × 3 × 2 × 1, which equals 120. Factorials are commonly used in permutations and combinations, helping to determine the number of ways to arrange or select items. The factorial of zero, 0!, is defined to be 1. This definition is useful in various mathematical contexts, including calculus and algebra. Factorials grow rapidly with increasing n, making them significant in fields such as statistics and computer science for solving complex problems.