## About Factorial Calculator Online

▪ A **factorial calculator online is a tool that can calculate the factorial of a given number.**

▪ A factorial of a number is the product of all positive integers from 1 to that number. For example, the factorial of 5 is 5 x 4 x 3 x 2 x 1 = 120.

▪ An online factorial calculator typically works by allowing the user to input a number and then use an algorithm to calculate the factorial. The calculator may provide the answer in real time or after a short delay, depending on the complexity of the calculation.

▪ Many factorial calculators also provide additional features, such as the ability to calculate factorials of large numbers, display the prime factorization of the number, or show the steps involved in the calculation.

▪ Online factorial calculators can be useful for a variety of applications, such as mathematics, statistics, engineering, and computer science. They can be accessed from any device with an internet connection, making them convenient for users who need to perform quick calculations on the go.

## Calculator Use

▪ Please use this calculator to calculate the factorial of a number:

- Enter an integer.
- Press the "Calculate" button.
- The factorial of the entered integer will be displayed.

## Factorial Formula

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

▪ Where n=0,1,2,3,4,..........

▪ Factorial of 10

10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800

▪ By definition, the factorial of 0, 0! = 1

## What is a Factorial?

▪ A factorial is a function that multiplies a number by every number below it.

▪ For example 5!= 5*4*3*2*1=120.

▪ The function is used, among other things, to find the number of ways “n” objects can be arranged.

▪ In mathematics, there are n! ways to arrange n objects in sequence.

▪ "The factorial n! gives the number of ways in which n objects can be permuted."[1]

▪ For example:

- 2 factorial is 2! = 2 x 1 = 2

-- There are 2 different ways to arrange the numbers 1 through 2. {1,2,} and {2,1}. - 4 factorial is 4! = 4 x 3 x 2 x 1 = 24

-- There are 24 different ways to arrange the numbers 1 through 4. {1,2,3,4}, {2,1,3,4}, {2,3,1,4}, {2,3,4,1}, {1,3,2,4}, etc. - 5 factorial is 5! = 5 x 4 x 3 x 2 x 1 = 120
- 0 factorial is a definition: 0! = 1. There is exactly 1 way to arrange 0 objects.

### Factorial Problem 1

**How many different ways can the letters in the word “document” be arranged?**

▪ For this problem we simply take the number of letters in the word and find the factorial of that number. This works because each letter in the word is unique and we are simply finding the maximum amount of ways 8 items can be ordered.

8!=8*7*6*5*4*3*2*1= **40,320**

### Factorial Problem 2

**How many different ways can the letters in the word “ positive” be arranged?**

▪ This problem is slightly different because there are two “i” letters.

▪ To account for this we divide by the number of duplicate letters factorial.

▪ There are 8 letters in the word **"Positive"** and two duplicate letters so we must find 8!/2!.

▪ If the word had multiple duplicates, as in “**infinity**,” the formula would be **8!/ (2! * 3!).**

8!/2!=(8*7*6*5*4*3*2*1)/(2*1)= **20160**