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# Factorial Mean in Math

November 30, 2022 written by Azhar Ejaz

Factorials are an important mathematical function that is used to find out how many different ways a set of things can be arranged. Daniel Bernoulli discovered the well-known interpolating function of the factorial function.

The factorial concept is a mathematical calculation that is used to determine the number of ways a certain event can occur. This concept is used in many different fields of mathematics, such as probability, permutations and combinations, sequences, and series. A factorial is a function that multiplies a number by every number below it, down to 1. So, the factorial of 3 would be the multiplication of numbers 3, 2, and 1 – i.e. 3! = 3 × 2 × 1. This would equal 6.

In this article, you will learn the mathematical definition of the factorial, how it’s written, the formula, examples, and so on in detail.

## What is Factorial?

The factorial of any whole number is the function that multiplies that number by every natural number below it. Symbolically, a factorial is represented by using the symbol “!”. So, “n factorial” means the product of the first n natural numbers and is represented as n!

Factorials are a mathematical concept often used in statistics and probability. In short, a factorial is the product of all the integers from 1 to a given number. For example, the factorial of 5 would be 1x2x3x4x5=120.

## Factorial Notation

The factorial of a positive integer is the product of all positive integers that are less than or equal to n. It is represented by the symbol n!

## Factorial Formula

The n factorial formula in math is a way to calculate the product of a given integer and all the integers below it. In other words, it helps you find the product of a given number and all the numbers below it.

The formula for n factorial is: n! = n × (n – 1)!

The formula to find the factorial of a number is:

n! = n × (n-1) × (n-2) × (n-3) × ….× 3 × 2 × 1

For example, if we want to find the factorial of 5, we would use the following calculation:

5! = 5 × 4 × 3 × 2 × 1 = 120

## Factorial of Number

To find the factorial of any given number, simply substitute the value for n in the following formula:

n! = n * (n-1) * (n-2) * … * 3 * 2 * 1

For example, the factorial of 5 would be calculated as follows:

5! = 5 * 4 * 3 * 2 * 1 = 120

## Use of factorial

Factorials are commonly used in permutations and combinations to determine the number of ways that a set of items can be arranged or the number of ways that a set of items can be selected.