Mathematics is considered the basis of every other scientific stream, e.g. Physics & Chemistry, etc. It has countless topics which will help us in every sphere of life. Factorial is one such topic that is used greatly in mathematics and in computers.
Hello Friends, Today we are going to find the answer to what is the value of 100 factorial. We will also try to find how factorial is calculated and what is its usage in real life. So friends let’s begin. Why it is considered so important in the field of computers and mathematics?
Table Of Contents
What is the Factorial of Hundred
First, let’s try to answer our original query for the value of 100 factorial. Here are the details of it-
100!=93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
i.e. 100!= 9.332621E+157. (it is a big number.. isn’t it? 🙂 )
What is Factorial
Firsts understand the definition of Fctorial before we deep dive into its examples and usage.
The Factorial of an Integer is nothing but the multiplication of that as well as all the lesser integers together.
For example, if we have to find the factorial of 4 (factorial 4 is written as 4!)
Then 4! Is 4*3*2*1=24
Similarly, if we have to find the factorial of 10 (Factorial 10 is written as 10!)
Then 10!= 10*9*8*7*6*5*4*3*2*1=3,628,800
Or in other words, if we have to find the Factorial of an Integer N
Then N!=N*(N-1)*(N-2)*(N-3)*(N-4)*………..3*2*1
Now coming back to our original question of what is the value of 100 factorial, we can also say that N!=N*!(N-1). This means to find the factorial of any integer we can multiply that integer with the factorial of one lesser integer. Or in simpler words, factorial is the product of all consecutive integers.
You can also find more about factorial at https://en.wikipedia.org/wiki/Factorial
We will understand the same with a few examples
Examples of Factorial
5!=5*4!= 5*4*3*2*1=120
Similarly 4!=4*3!=4*3*2*1=24
Hence 100!=100*99!
If someone ask you what is value of 100 factorial you can write the answer as follows-
100!=100*99*98*97*96*95*94*93*92*…………………..5*4*3*2*1
Hope you can now easily answer our original question which is What is the factorial of hundred?
Origin of Factorial
Though many scholars have linked factorial with many cultures however one of the first one and probably the earliest known descriptions of factorial was found in Jain literature around 300 BC.
Jain monks use factorials widely around the 6th Century and during the 11th Century. Great ancient Indian mathematician Bhāskara II also used factorials to describe various real-world scenarios.
Factorial can also be found in the mathematical literature of the Middle East during the era of 200 CE to 500 CE.
Pluto has used factorial during his era m however no further evidence can be found other than few examples.
Isn’t it amazing that the question What is the factorial of hundred is here since 300 BC … Be amazed with me 🙂
Use of Factorial
The earliest use of factorial was to calculate the permutations and combinations. The usage of Factorial in algebra was thought binomial theorem (Wikipedia ).
Factorial has his application in number theory as well. Sequential series and integration have also the use of factorials.
However, the most extensive use of Factorial can be found in probability theory.
The factorial function has various applications in mathematics and computer science. Here are some examples:
Combinatorics: The factorial function is widely used to count the number of different ways that any objects can be arranged in a certain order.
Permutations and combinations: Permuationa & Combination has wide usage of factorial. The factorial function is used to calculate the number of permutations and combinations of a set of objects.
Usage for designing the Algorithm: The factorial function is also been used in the analysis of algorithms, particularly which involves the time complexity of algorithms.
Hence the question What is the factorial of hundred can be answered through many branches of mathematics and computations.
FAQs of Factorial
In this section of FAQs, Let’s Discuss some questions that people generally ask about Factorial
How many zeros are the in the factorial of Hundred? Please specify.
While calculating the above-stated values, you will find that there are 24 Zeros in the Factorial of Hundred.
How many digits are there in the Factorial of 100?
There are 158 digits in the Factorial of Hundred.
What is the value of 0!
The value of 0! Is 1
Can we calculate the Factorial of fractions e.g. !(5.4)?
No, we can’t calculate the value of factorial of fractions, by definition factorial is the value of multiplying an integer with lesser possible integers.
How to calculate the Factorial of a negative number?
No, we can’t calculate the value of factorial of negative numbers, by definition factorial is the value of multiplying an integer with lesser possible integers.
What is a Factorial of Hundred?
The value of 100 factorial is 9.332621544 × 10^157.
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Hope with this post, we are able to answer our original question which is What is the factorial of hundred? Also, we have tried to answer other questions associated with factorial. If there are still any doubts left, feel free to drop a message.
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