# Factorial Calculator (n!)

Best free Online Factorial Calculator. Easiest Way to get the Factorial of the number.

In mathematical concepts, the end product of a given positive integer (n) or number is called the factorial of that number, which is denoted by ‘n!’. Factorial is also called the end product of an integer and all the integers fall under it.

For example : The factorial of Number 3 (3!) is equals to 6 (3 x 2 x 1= 6).

Factorial calculations are occured in many areas of maths just like in case of mathematical analysis, algebra, combinatorics etc. Earlier in 12th century ‘Indian Scholars’ started using the trend of factorial calculations for counting permutations.

In 1808 one of the well-known french mathematician ‘Christian Kramp’ introduced the notation of ‘n!’ for factorial.

## Factorial Calculator Use

• It is very simple to use this factorial calculator.
• You just have to enter the number in the factorial calculator in the first box.
• Your result i.e the factorial of entered number will be displayed in the second box.

## Formula to Find Factorial

The formula to calculate factorial of the positive integer is mentioned below:

For Example,

5! = 5 x 4 x 3 x 2 x 1 = 120.

### Basic Factorial Calculation Examples & Solution

Q1. A deck of playing cards has 13 hearts. There are how many ways with which these 13 hearts can be arranged ?

Solution :

The solution of this factorial problem is very easy. It involves calculating the factorial. As we want to know how these 13 cards of heart can be arranged, we need to calculate the value of 13 factorial ( 13! ).

13!= 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 6,227,020,800

Note : These calculations can be time consuming by solving with just pen and paper. So you can just head upto above factorial calculator and just get your answer within blinking your eye.

Q2. There are how many different ways with which the letters in the word ‘background’ can be arranged ?

Solution :

For solving this problem, we just have to take the number of letters in the given word and find the factorial of that number. In these problem all the letters in the given word are unique and non-repeated. Therefore total number of letters in the given word are 10, so we have to find the factorial of number 10.

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3.6288 E+6.

Q3. 8! x 5!

Solution :

Now in this problem to get the solution, we have to multiply the factorial of 8 with the factorial of 5.

Factorial of 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320

Factorial of 5! = 5 x 4 x 3 x 2 x 1 = 120

∴ 40320 x 120 = 4838400

Q4. 7! / 6!

Solution :

Now in this problem to get the solution, we have to divide the factorial of 7 with the factorial of 6.

Factorial of 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040

Factorial of 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

∴ 5040 / 720 = 7

Q5. There are how many different way that 8 people can come 1st, 2nd and 3rd?

Solution :

Now first let us name the numbers in alphabetically order. Let us assume that 8 people are called a, b, c, d, e, f, g, h then the list will go quite long.

∴ abc, abd, abe, abf, abg, abh, acb, acd, ace, acf, … etc.

The formula to solve this Factrorial Problem is 8!/(8-3)! = 8!/4!

Note: By using above factorial calculator you can easily get the factorials of 8 and 4. Now by writing the multiplies in full we get,

= ( 8 x 7 × 6 × 5 × 4 × 3 × 2 × 1 / 4 × 3 × 2 × 1 )
= ( 8 x 7 × 6 × 5 × 4 × 3 × 2 × 1 / 4 × 3 × 2 × 1 )
= 8 x 7 x 6 x 5 (remaining numbers get cancelled out each other)
= 1680

So there are almost 1680 ways that 8 people can come 1st, 2nd and 3rd.