Factorial Calculator

Factorial Calculator is a free online tool that displays the factorial of the number.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.

## Table of Contents

## 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**

Son!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! =12! = 2 × 1 =23! = 3 × 2 × 1 = 3 × 2! =64! = 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:

Number | Factorial |
---|---|

0 | 1 |

1 | 1 |

2 | 2 |

3 | 6 |

4 | 24 |

5 | 120 |

6 | 720 |

7 | 5,040 |

8 | 40,320 |

9 | 362,880 |

10 | 3,628,800 |

11 | 39,916,800 |

12 | 479,001,600 |

13 | 6,227,020,800 |

14 | 87,178,291,200 |

15 | 1,307,674,368,000 |

16 | 20,922,789,888,000 |

17 | 355,687,428,096,000 |

18 | 6,402,373,705,728,000 |

19 | 121,645,100,408,832,000 |

20 | 2,432,902,008,176,640,000 |

## 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 approximately9.33262154 × 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.