What is the factorial of 100

Factorial of 100 is 9.332621544E175 

hello everyone welcome to the learn here today's article is about what is the factorial of 100 and  a detailed method to calculate the factorial of 100

What is factorial

Factorial is the multiplication of a number in descending order values backward up to 1. Generally, we use factorial in the calculations of series sequences combinations and permutations 

Or in other words

Factorial is the mathematical function that multiplies a number by every number below from it up to 1.

Symbol of factorial

Factorial is denoted by a “!” sign

Formula of factorial

n! = n × (n-1) × ………. × 1

How to solve factorial?

It is very simple to find any numbers factorial just multiply every backward number like the below example

 

8! =7 × 6 × 5 × 4 × 3 × 2 × 1

So 8! = 40320

Similarly number 

7! =7 × 6 × 5 × 4 × 3 × 2 × 1

7! = 5040

What is the factorial of 100?

A factorial of 100 can be written as 100! And its direct answer is 9.332621544E175

100!=9332,62154,43944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864,000000000000000000000000

How do you solve 100 factorial?

Here is how to solve the factorial of 100!

If we want to solve it according to formulas then it will be a very time-consuming and lengthy process so to solve to factorize 100 into small numbers with their powers first of all we take the power of 2 then 3 and all of the prime numbers up to hundred like below

First of all, we factorize all the prime numbers up to 100 like below

100! = 2⁹⁷ × 3⁴⁸ × 5²⁴ × 7¹⁶ × 11⁹ × 13⁷ × 17⁵ × 24⁵ × 29⁴ × 31³ × 37² 41² × 43² × 47² × 53¹ × 59¹ × 61¹ × 67¹ × 71¹ × 73¹ × 79¹ × 83¹× 89¹× 97¹

All the prime factors above 50 like 53 59 61 67 71 73 709 83 89 97 have a power of 1 to prove it take anyone number from these and divide it by 100 like

100/53= 1 so do this for every number

All the prime factors above 33 and less than 50 (37 41 43 47) have a power of 2

Same way prime factors 29 and 31 have a power of 3

23 has a power of 4 another way to verify this method is to multiply 23 by 4 gives us 94 and if we multiply it by 5 then the number becomes greater than 100

Factors 17 and 19 have a power of 5

Prime factor 13 has the power of 7 because 13 time 7 is equal to 96 by increasing a number it becomes grates than 100

factors of 11

100/11= 9

Factor of 7

100/7 = 14/7 = 1 so 14+2 = 16 the power of 7 is 16

Factor of 5

100/5 = 20/5 = 4 so 20+4 = 24 the power of 5 is 24

Factor of 3

100/3 = 33/3 = 9/3= 3 so 33+9+3 = 48 the power of 3 is 48

Factor of 2

100/2 = 50/2 = 25/2 = 12/2 = 6/2 = 3/2=1 so 50+25+12+6+3+1 = 97 so 2 have power of 97

This is the easiest and quickest way to calculate the factorial of 100

FAQs 

how many digits are there in 100 factorial?

 

The total number in the factorial of 100 is 158

 

How many zeroes are there in 100 factorial?

number of trailing zeros in the factorial of 100 is 24

How to find the trailing zero?

Finding trailing zeros of any factorial number is a very long process but I will tell you a very short method in which you can easily find the number of zeros in any factorial number 

Divide 100 by 5 until it becomes less than

100/5 = 20

Now again divide 20 by 5

We get 4 which is less than 4

Now add all quotient 20+4 = 24

If you are astonished that how this method works then consider the below example

10= 5×2

From this can assume that any number ending with 0 has a factorial of 5×2

Just like

50 = 5×5×2

You can see above last factors have factors of 5×2

Any number which has zero in end has both theses factor 5×2  

So this is all concept behind this  

Conclusion:

 you know mathematics is all about practice no one can master it without mastering it so you must practice it as much as possible this was all about what is the factorial of 100 I hope you had got the concept of it