# [ Best Answer ] What is the factorial of hundred 100!

How to calculate what is the factorial of hundred: Factorial is a very important concept in mathematics and computer science. It was introduced by Carl Friedrich Gauss (1777–1855) in 1812 .The term factorial was coined by mathematician George Boole in 1854. He introduced the concept of multiplication into mathematics. In his book Mathematical Analysis of Logic (1847), he defined factorial as follows: “A factorial of a positive integer n is the product of all integers from 1 to n.”

In fact, it’s the basis of some algorithms that are used to solve problems. If you don’t know how to calculate factorial, then you might be wondering why it’s so difficult.

## What is Factorial?

Factorial of a number is a mathematical result that is achieved when the number for which it has to be calculated is multiplied by every number below it.

In other words it is the number multiplied by its power. In mathematics, the term ‘n!’ means n times itself, n squared, n cubed, etc., and is written !n. For example, 4!, meaning 4 times itself, is 24. Factorials are commonly used in combinatorics, probability, statistics, and calculus.

When you say the number multiplied by its own power (factorial) is the result of multiplying each factor by every other factor. For example, the factorial of 3 equals 1 x 2 x 3 =6. The factorial of 100 would equal 1 x 99 x 98 x 97 x 96… etc.

### Definitions of Factorial

Here are some definitions of factorial

• It is the product of its factors.
• The product of the natural numbers from 1 to n.
• Factorial of n is defined as the product of all positive integers from 1 to n.
• As the number of possible outcomes of an event or situation

### Formula of Factorial Calculation

The formula for calculating factorial is:

Factorial of N = N * (N-1) * (N-2) * (N-3)……..* (N-(N-1)

The symbol used for denoting factorial is !

For example 6!= 6*5*4*3*2*1=720.

Now using the same formula

Letting n = 100, we get

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

= 100 * 99 * 98 * 97 * … … * 1

93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

Essentially it denotes the number of ways “N” things can be arranged which is also called permutation and combination.

## Caluclate number of trailing zeros in Factorial

To calculate the number of zeros at the end of a factorial use these steps

step1- Recursively divide the number by 5 until the quotient is less than 5

Step 2- Sum the results after applying the greatest integer function.

The greatest integer function (usually denoted by brackets) is the rounded down integer of a value. For example,  = 6, [4.5] = 4, [-5.5] = -6.

So, Now calculation the number of trailing zeros in 100! is

([100/5]=20) + ([20/5]=4)

=>20 quotient + 4 quotient = 24.

So Factorial of 100 has 24 trailing zeros.

## Calculating 100! in Excel

We have formulas in Excel. To find the factorial of a given number, use the FACT() function in Excel.

Format the Excel cell column as number to see the full value which is 93326215443944200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.00

## Practical Uses of Factorial

Factorial has many applications in everyday life. For example, factorial is used to calculate the probability of events happening. Factors are very common in statistical analysis and they are just simply what we call numbers that indicate how many times something happens. Factors can range from 1-10.

### Example 1:

There are 12 people in a room. How many different seating arrangements are possible?

12! 12 choose 12 12 factorial is 10,368

### Example 2:

How many different ways can you arrange the letters in the word “factorial”?

This is a quiz for you . Once you understand the factorial concept you should be able to answer this question. Please reply in the comments.

## Computer Programs for calculating factorial of 100

So with this method let’s do our maths and make computer programs in C , Java python etc to solve the factorial of 100.

Below are some of the common programming languages used for calculating 100!.

### C program to find what is the factorial of hundred

To calculate 100! you can use the below C program for reference.

``````#include<stdio.h>
int main(){
int i,f=1,num;

printf("Enter a number: ");
scanf("%d",&num);

for(i=1;i<=num;i++)
f=f*i;

printf("Factorial of %d is: %d",num,f);
return 0;
}``````

### JAVA program for calculating 100 Factorial

``````class Facto{
public static void main(String args[]){
int i,fact=1;
int number=100;//It is the number to calculate factorial
for(i=1;i<=number;i++){
fact=fact*i;
}
System.out.println("Factorial of "+number+" is: "+fact);
}
}  ``````

### Python program for calculating Factorial of 100

``````def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n-1)
n=int(input("Input a number to compute the factiorial : "))
print(factorial(n))``````

### Using Javascript for 100 factorial

``````<!doctype html>
<html>
<script>
function show(){

var i, no, fact;
fact=1;
no=Number(document.getElementById("num").value);
for(i=1; i<=no; i++)
{
fact= fact*i;
}
}
</script>
<body>
Enter Num: <input id="num">
<button onclick="show()">Factorial equals</button>
</body>
</html>``````

## The Factorial Calculation Table till 100

### What number is factorial of 100?

F(100) = 100*99*…….*1 = 9.332622e+157

24

### What is the number of digits in 100 factorial?

The number of digits in 100 factorial is 158.

### What is the highest factorial?

Well, it’s actually undefined. We don’t know what the highest factorial is. However, we do know that factorial grows exponentially. That means that the higher the number, the faster it grows. And, since factorial grows exponentially, then the answer to our question is infinite.

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