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.

What is the 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)!

Factorial Formula
Factorial Formula

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:

Factorials
Factorials

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:

NumberFactorial
01
11
22
36
424
5120
6720
75,040
840,320
9362,880
103,628,800
1139,916,800
12479,001,600
136,227,020,800
1487,178,291,200
151,307,674,368,000
1620,922,789,888,000
17355,687,428,096,000
186,402,373,705,728,000
19121,645,100,408,832,000
202,432,902,008,176,640,000
Factorial table from 0 to 20

What is the Factorial of 100?

What is the Factorial of 100
Answer for "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.

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