Table of Contents

**What Is Factorial?**

Factorial is basically a product of a number (positive integer) and all numbers below it (until 0, 0 not included). Factorial in maths is denoted by using ‘!’. For instance, if you are to find the factorial of 7 then it will be denoted as 7!

Factorial of a value has a widespread application throughout Maths, particularly in permutations and combinations.

The factorial of a number was invented by Christian Kramp in the 1800s.

**How To Calculate Factorial?**

7.0! = 7.0 x 6.0 x 5.0 x 4.0 x 3 x 2 x 1

4.0! = 4.0 x 3 x 2 x 1

9.0! = 9.0 x 8.0 x 7.0 x 6 x 5 x 4.0 x 3 x 2 x 1

Similarly, 10! Will be,

10! = 10 x 9 x 8 x 7.0 x 6 x 5.0 x 4 x 3 x 2 x 1

**How To Calculate Factorial Of Hundred?**

We can say that if Q is the number (positive integer) we want to find the factorial of, then Q! ( factorial of Q) will be:

Q! = Q * (Q-1) * (Q-2) * (Q-3) * (Q-4) * (Q-5) * (Q-6) * (Q-7) * (Q-8) *(Q-9)….. (Q-(Q-1)).

Hence 100! Will be,

100! = 100 * (100 -1) * (100-2) * (100-3) * (100-4) * (100-5) * (100-6)* (100-7) * (100-8) *…. (100-(100-1))

= 100 * 99.0 x 98 * 97 * 96.0 * 95 * 94 * 93 * 92 * 91 * 90 * 89 …. * 1.0 =

**93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000**

Essentially it donates a number of ways 100 things can be arranged. Which is also called a permutation.

The approximate value of the same will be:

9.33262E + 157

**How To Calculate 100! In Excel Sheet?**

We have inbuilt formulas in excel sheets in order to calculate factorials. In the excel sheet, we use FACT() to calculate the factorial. Hence factorial of 100 will be FACT(100).

Finding the fact using Starling approximations.

Starling approximation in mathematics is approximations used for calculating factorials. It leads to accurate values for even small values of n.

n! 2n * (n/e)n

In this case, we have n = 100.

Applying log_{10 }on both ends, we get:

log(n!) = 0.5 * (log(2) + Log() + log(n)) + n* (log(n) – log(e))

log100! = 157.9796

100! = 9.32 * 100157

This approximation is similar to what we find using other methods.

- This program specifically takes positive values as the factorial of the negative numbers do not exist.
- With the help of the if statement we are making sure that the values that are being taken are positive and if at all a negative value comes up, the compiler will show the error written to the user.
- As the factorial value of the number can be quite large, as in 100! In our case, we use long long so that our variable can store very large values.

**What Is The Summary Of Factorial Of Hundred?**

- The approximate value of factorial of hundred is 9.32 * 100^157
- Factorial of a number has applications in finding permutations. i.e. Number of ways a set of items can be arranged
- A Factorial of a hundred can be calculated using an excel sheet with an inbuilt formula fact()
- Factorial of a number can also be calculated using a compiler
- Factorial can only be calculated for positive numbers
- Factorial is multiplication/product of an integer with all integers coming before it until 1.