What is Factorial?
Factorial is the product of n numbers until it reaches up to 1. It we want to calculate the factorial of n, then we multiply the number less than or equal to n until it encounters 1. In other words, the multiplication of 1 to n is called the factorial of n.
The factorial of the number n can be also defined as the product of the number n and the factorial (n -1).
Factorial Notation
The notation of the factorial is “!” or “⌋”. If we have to find the factorial of the number n then, it is written as n! or n⌋.
Let’s consider some examples of factorials:
- 5! = 5 × 4 × 3 × 2 × 1 = 120
- 4! = 4 × 3 × 2 × 1 = 24
- 3! = 3 × 2 × 1 = 6
- 2! = 2 × 1 = 2
- 1! = 1
Factorial of 0
As a factorial is defined as the product of natural numbers up to the number under consideration, but in the case of 0, if we were to follow the same definition, it would result in 0. However, this would lead to inconsistencies with many already proven results. Therefore, factorial is initially defined in such a way that the factorial of 0 is 1. This definition makes sense on a larger scale, and we have further demonstrated its validity. As we generalize factorials into gamma functions, the result remains the same.
Thus, the factorial of 0 is defined as 1 and is represented as 0!
Factorial
Factorial is a fundamental concept in combinatorics as factorials play important roles in various mathematical formulas such as permutations, combinations, probability, and many other formulas. Factorial of any natural number “n” is defined as the product of all natural numbers till n.
In this article, we’ll delve into the intricacies of factorials, exploring factorial notation, the diverse range of factorial formulas, and techniques for computing factorials. Additionally, we’ll touch upon the properties and practical applications of factorials, provide illustrative examples, and address common questions pertaining to this topic. Let’s embark on our journey of understanding factorials.
Table of Content
- What is Factorial?
- Factorial Formula
- How to Find Factorial of a Number?
- Factorial Examples
- Properties of Factorial
- Factorials 1 to 20
- Applications of Factorials
- Solved Examples on Factorial