# What is the factorial

Here you can find answers to questions like: What is the factorial of 100? What is the factorial of 100? What is the last digits of factorial of 100? How many trailing zeros in 100 factorial? How many digits are there in 100 factorial? Use the factorial calculator above to find the factorial of any natural between 0 and 10,000.

## What is the factorial

### Definition of factorial

The factorial is a quantity defined for any integer n greater than or equal to 0.

The factorial is the product of all integers less than or equal to n but greater than or equal to 1. The factorial value of 0 is by definition equal to 1. For negative integers, factorials are not defined. The factorial can be seen as the result of multiplying a sequence of descending natural numbers (such as 3 × 2 × 1).

The factorial symbol is the exclamation mark !.

### The factorial formula

If n is a natural number greater than or equal to 1, then

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

If n = 0, then n! = 1, by convention.

Example: 7! = 7 x 6 x 5 x 3 x 2 x 1 = 1260

#### Step-by-step explanation

We know that if n be a number, then its factorial is given by

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

Here our given number is 100. Thus taking n = 100, we get

100! = 100 × (100 – 1) × (100 – 2) × (100 – 3) × … … × 1

= 100 × 99 × 98 × 97 × … … × 1

93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

Let us find the factorial of a smaller number. Say, n = 4. Then 4! = 4 × 3 × 2 × 1 = 24.