Factorial

What is Factorial in Math?

Factorial of a number is the product of numbers less than n up to 1.

What is the Formula for the Factorial of any Number n?

The formula for the factorial is given by:

n! = n × (n -1) × (n – 2) … 3 × 2 × 1

How is a Factorial Calculated?

To calculate factorial of any number n i.e., n!, multiply all integers from 1 to n together. For example, 3! = 3 × 2 × 1 = 6.

What is the Value of 0!?

The value of factorial zero i.e., 0! = 1.

What is the Notation of Factorial?

The notation of factorial is !

Why Factorial is Used?

The factorial is used in permutations, combinations, binomial theorem, probability etc.

What is the Purpose of Factorials?

The purpose of factorials is to represent the product of all positive integers from 1 to a given number, commonly used in combinatorics and mathematical calculations.

Can Factorials be Calculated for Non-Integer Values?

Factorials are defined for non-negative integers only, while the gamma function, an extension of factorials, is defined for all non-integer values.

What is Factorial of 5?

Factorial of 5 is denoted by 5! or 5⌋ and is equal to 120.

What is the value of 6 Factorial?

The value of factorial is 6! = 720

What is Factorial of 7?

Factorial of 7 is denoted by 7! and is equal to 5040.

What is factorial of 100?

Factorial of 100 is 9.33262154 × 10¹⁵⁷.

What is the value of 4 Factorial?

The value of 4 Factorial is 4! = 120

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.