Knowledge

# The factorial of 100 is a huge number, but did you know that it’s actually quite easy to calculate?

Rate this post

In mathematics, the factorial of a non-negative integer n is the product of all positive integers less than or equal to n. It is denoted by n!. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120 and 4! = 4 × 3 × 2 × 1 = 24. Factorials are often used to describe the number of possible outcomes in certain situations, such as the number of possible outcomes when two dice are rolled or the number of possible outcomes when two fair coins are flipped simultaneously.

### Introduction What is the factorial of 100

The function n! (read n factorial) produces the product of all positive integers less than or equal to n. In other words, write a factorial as n*(n-1)*(n-2)*…*2*1. For example: 5! = 5*4*3*. Writing out every single integer from 1 up to 100 would take far too long; fortunately, there’s an easier way.

## Why do we use this algorithm?

Before we talk about why we use Knuth’s Algorithm, let’s go over what factorials are. To put it simply, if we have n = 100 and want to find out how many numbers from 1 – 100 are divisible by 4 we multiply those two numbers together.

## An example using 10

10! can be calculated by multiplying 10*9*8*7…all way down to 1. In other words: 10! = 10·9·8·7…1. So 10! = 3628800.

### Step-by-step explanation

We know that if n is 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.