### What is Factorial?

The concept of Factorials was given in Algebra and further, they can be used for statistics, permutation, combinations, and to calculate the probabilities. Wherever you see the exclamation symbol(!) behind an integer, this is a factorial.

## Factorial Formula

The Factorial formula is generally defined as the product of given number with all lowest vale numbers. This is denoted by Factorial (!) exclamation symbol. This is also taken as the series of number in descending order. The factorial formula is generally required in permutation and combinations to calculate the probabilities.

For the integer greater than or equal to one, the factorial formula is mathematical is generalized as given below.

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

*If p = 0, then p! = 1 by convention.*

\[\LARGE n! \; = 1 \; \times 2 \; \times 3 \; \times ….. \; \times \; (n-1) \; \times n\]

Factorials can be defined for all integers whose values are taken as greater than zero. For the integer greater than or equal to one, the factorial would be the multiplication of all lowest numbers. In case of non-negative integers, the Factorial formula is not applicable.

### Factorial of a Number

Calculation of factorial of a number is easy. For example, 4! In mathematics is “six factorials.” Based on the formula it could be elaborated as –

4! = 4 x 3 x 2 x 1 = 24

Thus, Factorial of a number 4 is 24 here.

### Factorial Function

From the arithmetic point of view, Factorial functions are needed to showcase fixed-sized integers and avoids the overflows of data. They are frequently used for complex computer problems and difficult to calculate manually without a proper understanding of the concept. If this is not possible to calculate the factorial of a number directly then it is generally broken down into parts to make the calculation easy.

There are a variety of mathematical applications where factorial can be calculated directly but still, you should know the basics to solve real-world problems quickly on your fingertips. Take an example, if you are preparing for competitive exams then do automatic computer programs are fruitful there? Obviously, No!

Here, you should know the Factorial concept in detail, and its basic formulas, factorial function, factorial equations etc. Also, do practice a number of questions to solve difficult problems with ease. They are the part of higher studies too where students are planning to join mathematics course during their graduation or post-graduation studies.

### Factorial equation

Factorial equations are the expressions in mathematics where basic formulas are used to compute the final outcome. For n factorial, there is n number of possible ways of arranging a number. They are into existence since 12^{th} centuries and used for a plenty of daily applications too. The notation of factorial was suggested by a popular French mathematician Christian Kramp in 1808. In certain case, the definition of a factorial function can also be extended to non-integer arguments while keeping important properties the same. This is generally studied in advanced mathematics for analysis of concepts.