Properties of Factorial
Some of the properties of factorial are:
- For any non-negative integer n,
- n! = n × (n – 1) × (n – 2) × … × 3 × 2 × 1
- Factorial can be defined recursively as follows:
- n! = n(n – 1)! [ Where 0! = 1]
- 0! is defined to be 1 by convention.
- For any non-negative integer n, n! is always an integer.
- As ∏ is used to represent product of terms in sequence, thus factorial of n can also be represented as:
- n! = ∏(i = 1 to n) i.
- Factorial of negative numbers are undefined.
- The factorial of large numbers can grow very rapidly. For example, 10! = 3,628,800, 15! = 1,307,674,368,000, and so on.
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