# What is 21 factorial ?

Steps to calculate factorial of 21

## How to calculate the factorial of 21

To find 21 factorial, or 21!, simply use the formula that multiplies the number 21 by all positive whole numbers less than it.

Let's look at how to calculate the Factorial of Twenty-one :

21! is exactly : 51090942171709440000

Factorial of 21 can be calculated as:
21! = 21 x 20 x 19 x 18 x ... x 3 x 2 x 1

The number of trailing zeros in 21! is 4

The number of digits in 21 factorial is 20.

## What Is Factorial?

A factorial is showed by an integer and an exclamation symbol. In arithmetic, factorial is a multiplication operation of natural numbers .

It multiplies the number by every organic number that is less than it .

Symbolically, it is displayed as "!".

The function is used, among other things, to get the "n" way pieces can be positioned .

## Factorial Formula

To find the factorial of any given number, change the exact value for n in the given formula :

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

The expansion of the formula provides the numbers to be replicated together with each other to find the factorial of the number.

We can also calculate a factorial from the previous one. The factorial of any number is that number times the factorial of (that number minus 1).

So the rule is : n! = n × (n−1)!

Example :
21! Factorial = 21 x 20 x 19 x 18 x ... x 3 x 2 x 1 = 21 × 20! = 51090942171709440000

## What are Factorials Used For?

The best use of factorial is in Combinations and Permutations.

Example : Determine how to arrange letters without repeating?

There one way for 1 letter "a":
2 ways for two letters "ab": ab, ba.
There are 6 ways for 3 letters "abc": abc acb cab bac bca.
There are 24 ways for 1234 of the letters "abcd"

## Frequently Asked Questions on Factorial

### Can we have factorials for negative numbers ?

Negative integer factorials are undefined

### What Is 0!

Zero factorial or Factorial of 0 is simple, and its value is equal to 1. So, 0! = 1.