Factorial Calculator

The factorials calculator is an online statistics tool that finds factorial of any number n using the correct factorial formula. 

The bigger answers are represented in e notation. You also get the calculation of the factorial using this tool.

What is a factorial?

Wikipedia defines factorial as:

“The factorial of a non-negative integer n is the product of all positive integers less than or equal to n” 

In a factorial, the number is multiplied by all the numbers less than the number till 1, no negative integers included. 

In mathematics, the exclamation mark (!) is used to represent factorial. Factorials are used in probability problems like permutations and combinations.

Factorial Formula

The factorial formula of n integer is:

n! = n x (n-1) x (n-2) x … x 1.

According to this formula, 5 factorial is:

5! = 5 x 4 x 3 x 2 x 1

This equation can be also written as;

5! = 5 x (4 x 3 x 2 x 1)

5! = 5 x (4!) 

We can make a general equation from the previous conclusion as:

n! = n x (n-1)!

The factorial of both 0 and 1 is 1. The reason why 0! is 1 is a whole pandora box. But one thing you should know is that it is a convention so that other factorials can be calculated accurately.

How to solve factorials?

Factorials are easy to calculate but their drawback is that they take time, as most of the math does. That is what makes the factorial calculator important and useful.

Example:

Solve:

6!, 4!, and 7! 

Solution:

6! = 6 x 5 x 4 x 3 x 2 x 1

= 720

4! = 4 x 3 x 2 x 1

= 24

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1

= 5,040

There are little more complex factorial equations that can be solved easily enough if you know how factorials work. Let’s solve an example.

Example:

Find n;

(n-2)! / (n-4)! = 30 where n ≥ 1.

Solution:

As you know n! = n(n-1)!, this formula can be used to expand (n-2)! in such a way that can simplify the equation to some extent. So, 

(n-2)! = (n-2)(n-2-1)! 

(n-2)! = (n-2)(n-3)!

Again doing so.

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

(n-2)! = (n-2)(n-3)(n-4)!

Putting this in the equation, we get.

(n-2)(n-3)(n-4)! / (n-4)! = 30

(n-2)(n-3) = 30

n² - 3n - 2n + 6 = 30

n² - 5n + 6 = 30

n² - 5n - 24 = 0

By factoring the equation: 

n² - 8n + 3n - 24 = 0

n(n - 8) + 3(n - 8) = 0

(n + 3)(n - 8) = 0

n = -3 , n = 8

As n ≥ 3 this means n = -1 is invalid. Hence the correct answer is n = 8.