# What is the Factorial of Hundred (100)? Free Factorial Calculator

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What is the Factorial of Hundred (100)?- the value of Factorial 100 comes out to be equal to 9.332622e+157. Check here The exact value of factorial of hundred.

## Answer of "What is the factorial of hundred (100)"

• 100! is exactly: 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
• The approximate value of 100! is 9.3326215443944E+157.
• The number of trailing zeros in 100! is 24.
• The number of digits in 100 factorial is 158.
• The factorial of 100 is calculated, through its definition, this way:
100! = 100 x 99 x 98 x 97 x 96 . . . 3 x 2 x 1

## What is Factorial?

Factorial is a mathematical function denoted by the exclamation mark (!). It is used to calculate the product of all positive integers from 1 up to a given number.

Example

The factorial of 5 (written as 5!) is the product of all positive integers from 1 to 5: `1 × 2 × 3 × 4 × 5 = 120`.

```So n! or "n factorial" means:

n! = 1 x 2 x 3 x . . . x n
Product of the first n positive integers = n(n-1)(n-2) . . . . . . . . . . . . (3)(2)(1)  ```

### What is the Factorial Formula?

The formula for n factorial can be expressed as `n! = n × (n - 1)!`

This means that the factorial of any number is equal to the given number multiplied by the factorial of the previous number.

For example, 8! = 8 × 7!, and 9! = 9 × 8!. To calculate the factorial of 10, we can use the formula 10! = 10 × 9! Similarly, if we have (n+1) factorial, it can be written as (n+1)! = (n+1) × n!.

The following examples demonstrate the use of the factorial formula.

5 Factorial

The value of 5 factorial is 5×4×3×2×1 which is equal to 120.
We can evaluate it using the factorial formula as well.
5! = 5 × 4! = 5 × 24 = 120.

7 Factorial

7 factorial is nothing but 7 × 6 × 5 × 4 ×3 × 2 × 1 = 5,040.

0 Factorial

Zero factorial is interesting, and its value is equal to 1, i.e., 0! = 1. Yes, the value of 0 factorial is NOT 0, but its 1.

```Let us see that how this works:

1! = 1
2! = 2 × 1 = 2
3! = 3 × 2 × 1 = 3 × 2! = 6
4! = 4 × 3 × 2 × 1 = 4 × 3! = 24```

Let’s go to the basic formula of factorial n! = n × (n - 1)!
How to find 3! What you do is 4! / 4.
Similarly, 2! is 3! / 3, and so on.
Now, let’s look at the pattern:

In this way, we could prove that 0 factorial is 1.

Another method to prove that 0! is equal to 1 involves the concept of permutations.

In permutations, we learn that `n!` represents the number of ways in which `'n'` distinct items can be arranged. From this perspective, it can be argued that 1! equals 1 since there is only one possible arrangement of one item. Similarly, since there is only one possible arrangement of no items, 0!, too, equals 1.

### Use of Factorial

Factorials are widely used in the field of mathematics, particularly in permutations and combinations.

• Permutation is an ordered arrangement of outcomes and it can be calculated with the formula: n Pr = n! / (n - r)!
• Combination is a grouping of outcomes in which order does not matter. It can be calculated with the formula: nCr = n! / [ (n - r)! r!]

Example 1: How many ways can three coins be arranged if tossed at the same time?

Solution: 3! = 3 × 2 × 1 = 6
HTH, HTT, HHT, THT, TTH, THH
In this way you can find the result of any game.

You can also read "How Many Ounces in a Cup? Complete Guide"

### Calculation of Factorial

Here's a factorial table from 0 to 20:

## What is the Factorial of 100?

```The factorial of 100 is denoted as 100! and it can be calculated as:

`100! = 100 x 99 x 98 x 97 x 96 x ... x 2 x 1`

This means multiplying all the numbers from 1 to 100. However, manually calculating the factorial of such a large number is not feasible, even with a calculator.

To calculate 100!, we can use the Stirling's approximation, which is given by:

`n! ≈ √(2πn) * (n/e)^n`

where n is the number for which we want to calculate the factorial, e is Euler's number (approximately equal to 2.71828), and π is the mathematical constant pi (approximately equal to 3.14159).

Using this formula for n = 100, we get:

`100! ≈ √(2π*100) * (100/e)^100`

`100! ≈ 9.33262154 × 10^157`

Therefore, the factorial of 100 is approximately 9.33262154 × 10^157```
`100!=93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000`

## Factorial of Negative Numbers

Can we have factorials for numbers like −1, −2, etc? Let's start with 3! = 3 × 2 × 1 = 6

3! = 3 × 2 × 1 = 6
2! = 3! / 3 = 6 / 3 = 2
1! = 2! / 2 = 2 / 2 = 1
0! = 1! / 1 = 1 / 1 = 1
(- 1)! = 0! / 0 = 1 / 0 = dividing by zero is undefined

And from here on down all integer factorials are undefined. So, negative integer factorials are undefined.

## Program of factorial in C language?

Here's an example program of factorial in C to calculate the factorial of a number:

```#include <stdio.h>

int main() {
int num, i;
unsigned long long factorial = 1;

printf("Enter an integer: ");
scanf("%d", &num);

if (num < 0) {
printf("Error: Factorial of negative number doesn't exist.\n");
} else {
for (i = 1; i <= num; ++i) {
factorial *= i;
}
printf("Factorial of %d = %llu\n", num, factorial);
}

return 0;
}```

This program prompts the user to enter an integer. Then calculates the factorial of the number using a loop, and then prints the result. It also includes error checking for negative input values, which don't have a defined factorial.

## FAQ

### What is the Factorial of Hundred?

Factorial of 100 is approximately 9.33262154 × 10^157.

### How big is 10 factorial?

The value of factorial of 10 is 3628800, i.e. 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3628800.

### What is the highest factorial?

The last factorial is 170! “Did you know? The number 170 is the highest possible number you can calculate a factorial for? Any higher than 170, and the mathematical answer is infinity.”

### What is the factorial of 100 with voice?

The approximate value of 100! is 9.3326215443944E+157. The number of trailing zeros in 100! is 24.

### What is factorial of 5?

The factorial of 5 is 120. This is because 5! (read as "5 factorial") is calculated as: 5! = 5 x 4 x 3 x 2 x 1 = 120

## Conclusion

Factorials are a powerful mathematical tool that can be used in a variety of applications. From permutations and combinations to probability and statistics.

The factorial of a number is the product of all positive integers less than or equal to that number. It can be calculated using a simple formula(n! = n × (n - 1)!).

In this article, we explored the concept of factorials. Learned how to calculate the factorial of a number, and examined some of the applications of factorials in different fields.