[ Best Answer ] What is the factorial of hundred 100!

What is the factorial of hundred
100!

How to calculate what is the factorial of hundred: Factorial is a very important concept in mathematics and computer science. It was introduced by Carl Friedrich Gauss (1777–1855) in 1812 .The term factorial was coined by mathematician George Boole in 1854. He introduced the concept of multiplication into mathematics. In his book Mathematical Analysis of Logic (1847), he defined factorial as follows: “A factorial of a positive integer n is the product of all integers from 1 to n.”

In fact, it’s the basis of some algorithms that are used to solve problems. If you don’t know how to calculate factorial, then you might be wondering why it’s so difficult.

What is Factorial?

Factorial of a number is a mathematical result that is achieved when the number for which it has to be calculated is multiplied by every number below it.

In other words it is the number multiplied by its power. In mathematics, the term ‘n!’ means n times itself, n squared, n cubed, etc., and is written !n. For example, 4!, meaning 4 times itself, is 24. Factorials are commonly used in combinatorics, probability, statistics, and calculus.

When you say the number multiplied by its own power (factorial) is the result of multiplying each factor by every other factor. For example, the factorial of 3 equals 1 x 2 x 3 =6. The factorial of 100 would equal 1 x 99 x 98 x 97 x 96… etc.

Definitions of Factorial

Here are some definitions of factorial

  • It is the product of its factors.
  • The product of the natural numbers from 1 to n.
  • Factorial of n is defined as the product of all positive integers from 1 to n.
  • As the number of possible outcomes of an event or situation
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Formula of Factorial Calculation

The formula for calculating factorial is:

Factorial of N = N * (N-1) * (N-2) * (N-3)……..* (N-(N-1)

The symbol used for denoting factorial is !

For example 6!= 6*5*4*3*2*1=720.

Now using the same formula

Letting n = 100, we get

100! = 100 * (100 – 1) * (100 – 2) * (100 – 3) * … … * 1

= 100 * 99 * 98 * 97 * … … * 1

93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

Essentially it denotes the number of ways “N” things can be arranged which is also called permutation and combination.

Caluclate number of trailing zeros in Factorial

To calculate the number of zeros at the end of a factorial use these steps

step1- Recursively divide the number by 5 until the quotient is less than 5

Step 2- Sum the results after applying the greatest integer function.

The greatest integer function (usually denoted by brackets) is the rounded down integer of a value. For example, [6] = 6, [4.5] = 4, [-5.5] = -6.

So, Now calculation the number of trailing zeros in 100! is

([100/5]=20) + ([20/5]=4)

=>20 quotient + 4 quotient = 24.

So Factorial of 100 has 24 trailing zeros.

Calculating 100! in Excel

We have formulas in Excel. To find the factorial of a given number, use the FACT() function in Excel.

factorial of 100 in Excel
Use formula fact(100) to calculate factorial of 100 in Excel
image 2

Format the Excel cell column as number to see the full value which is 93326215443944200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.00

Practical Uses of Factorial

Factorial has many applications in everyday life. For example, factorial is used to calculate the probability of events happening. Factors are very common in statistical analysis and they are just simply what we call numbers that indicate how many times something happens. Factors can range from 1-10.

See also  What is secent of a circle?

Example 1:

There are 12 people in a room. How many different seating arrangements are possible?

Answer:

12! 12 choose 12 12 factorial is 10,368

Example 2:

How many different ways can you arrange the letters in the word “factorial”?

This is a quiz for you . Once you understand the factorial concept you should be able to answer this question. Please reply in the comments.

Alexa vs Siri Vs Bixby Vs Google , How they answer What is the factorial of 100? Have Fun

When answering the question Alexa seems to answer the best while google has the most funny answer. Amused.

Computer Programs for calculating factorial of 100

So with this method let’s do our maths and make computer programs in C , Java python etc to solve the factorial of 100.

Below are some of the common programming languages used for calculating 100!.

C program to find what is the factorial of hundred

To calculate 100! you can use the below C program for reference.

#include<stdio.h>
int main(){
  int i,f=1,num;
 
  printf("Enter a number: ");
  scanf("%d",&num);
 
  for(i=1;i<=num;i++)
      f=f*i;
 
  printf("Factorial of %d is: %d",num,f);
  return 0;
}

JAVA program for calculating 100 Factorial

class Facto{  
 public static void main(String args[]){  
  int i,fact=1;  
  int number=100;//It is the number to calculate factorial    
  for(i=1;i<=number;i++){    
      fact=fact*i;    
  }    
  System.out.println("Factorial of "+number+" is: "+fact);    
 }  
}  

Python program for calculating Factorial of 100

def factorial(n):
    if n == 0:
        return 1
    else:
        return n * factorial(n-1)
n=int(input("Input a number to compute the factiorial : "))
print(factorial(n))

Using Javascript for 100 factorial

<!doctype html>
<html>
<head>
<script>
function show(){

var i, no, fact;
fact=1;
no=Number(document.getElementById("num").value);
for(i=1; i<=no; i++)  
{
fact= fact*i;
}  
document.getElementById("answer").value= fact;
}
</script>
</head>
<body>
Enter Num: <input id="num">
<button onclick="show()">Factorial equals</button>
<input id="answer">
</body>
</html>

The Factorial Calculation Table till 100

1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
7! = 5040
8! = 40320
9! = 362880
10! = 3628800
11! = 39916800
12! = 479001600
13! = 6227020800
14! = 87178291200
15! = 1307674368000
16! = 20922789888000
17! = 355687428096000
18! = 6402373705728000
19! = 121645100408832000
20! = 2432902008176640000
21! = 51090942171709440000
22! = 1124000727777607680000
23! = 25852016738884976640000
24! = 620448401733239439360000
25! = 15511210043330985984000000
26! = 403291461126605635584000000
27! = 10888869450418352160768000000
28! = 304888344611713860501504000000
29! = 8841761993739701954543616000000
30! = 265252859812191058636308480000000
31! = 8222838654177922817725562880000000
32! = 263130836933693530167218012160000000
33! = 8683317618811886495518194401280000000
34! = 295232799039604140847618609643520000000
35! = 10333147966386144929666651337523200000000
36! = 371993326789901217467999448150835200000000
37! = 13763753091226345046315979581580902400000000
38! = 523022617466601111760007224100074291200000000
39! = 20397882081197443358640281739902897356800000000
40! = 815915283247897734345611269596115894272000000000
41! = 33452526613163807108170062053440751665152000000000
42! = 1405006117752879898543142606244511569936384000000000
43! = 60415263063373835637355132068513997507264512000000000
44! = 2658271574788448768043625811014615890319638528000000000
45! = 119622220865480194561963161495657715064383733760000000000
46! = 5502622159812088949850305428800254892961651752960000000000
47! = 258623241511168180642964355153611979969197632389120000000000
48! = 12413915592536072670862289047373375038521486354677760000000000
49! = 608281864034267560872252163321295376887552831379210240000000000
50! = 30414093201713378043612608166064768844377641568960512000000000000
51! = 1551118753287382280224243016469303211063259720016986112000000000000
52! = 80658175170943878571660636856403766975289505440883277824000000000000
53! = 4274883284060025564298013753389399649690343788366813724672000000000000
54! = 230843697339241380472092742683027581083278564571807941132288000000000000
55! = 12696403353658275925965100847566516959580321051449436762275840000000000000
56! = 710998587804863451854045647463724949736497978881168458687447040000000000000
57! = 40526919504877216755680601905432322134980384796226602145184481280000000000000
58! = 2350561331282878571829474910515074683828862318181142924420699914240000000000000
59! = 138683118545689835737939019720389406345902876772687432540821294940160000000000000
60! = 8320987112741390144276341183223364380754172606361245952449277696409600000000000000
61! = 507580213877224798800856812176625227226004528988036003099405939480985600000000000000
62! = 31469973260387937525653122354950764088012280797258232192163168247821107200000000000000
63! = 1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000
64! = 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000
65! = 8247650592082470666723170306785496252186258551345437492922123134388955774976000000000000000
66! = 544344939077443064003729240247842752644293064388798874532860126869671081148416000000000000000
67! = 36471110918188685288249859096605464427167635314049524593701628500267962436943872000000000000000
68! = 2480035542436830599600990418569171581047399201355367672371710738018221445712183296000000000000000
69! = 171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000
70! = 11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000
71! = 850478588567862317521167644239926010288584608120796235886430763388588680378079017697280000000000000000
72! = 61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000
73! = 4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000000
74! = 330788544151938641225953028221253782145683251820934971170611926835411235700971565459250872320000000000000000
75! = 24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000
76! = 1885494701666050254987932260861146558230394535379329335672487982961844043495537923117729972224000000000000000000
77! = 145183092028285869634070784086308284983740379224208358846781574688061991349156420080065207861248000000000000000000
78! = 11324281178206297831457521158732046228731749579488251990048962825668835325234200766245086213177344000000000000000000
79! = 894618213078297528685144171539831652069808216779571907213868063227837990693501860533361810841010176000000000000000000
80! = 71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000
81! = 5797126020747367985879734231578109105412357244731625958745865049716390179693892056256184534249745940480000000000000000000
82! = 475364333701284174842138206989404946643813294067993328617160934076743994734899148613007131808479167119360000000000000000000
83! = 39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000
84! = 3314240134565353266999387579130131288000666286242049487118846032383059131291716864129885722968716753156177920000000000000000000
85! = 281710411438055027694947944226061159480056634330574206405101912752560026159795933451040286452340924018275123200000000000000000000
86! = 24227095383672732381765523203441259715284870552429381750838764496720162249742450276789464634901319465571660595200000000000000000000
87! = 2107757298379527717213600518699389595229783738061356212322972511214654115727593174080683423236414793504734471782400000000000000000000
88! = 185482642257398439114796845645546284380220968949399346684421580986889562184028199319100141244804501828416633516851200000000000000000000
89! = 16507955160908461081216919262453619309839666236496541854913520707833171034378509739399912570787600662729080382999756800000000000000000000
90! = 1485715964481761497309522733620825737885569961284688766942216863704985393094065876545992131370884059645617234469978112000000000000000000000
91! = 135200152767840296255166568759495142147586866476906677791741734597153670771559994765685283954750449427751168336768008192000000000000000000000
92! = 12438414054641307255475324325873553077577991715875414356840239582938137710983519518443046123837041347353107486982656753664000000000000000000000 td>
93! = 1156772507081641574759205162306240436214753229576413535186142281213246807121467315215203289516844845303838996289387078090752000000000000000000000
94! = 108736615665674308027365285256786601004186803580182872307497374434045199869417927630229109214583415458560865651202385340530688000000000000000000000
95! = 10329978488239059262599702099394727095397746340117372869212250571234293987594703124871765375385424468563282236864226607350415360000000000000000000000
96! = 991677934870949689209571401541893801158183648651267795444376054838492222809091499987689476037000748982075094738965754305639874560000000000000000000000
97! = 96192759682482119853328425949563698712343813919172976158104477319333745612481875498805879175589072651261284189679678167647067832320000000000000000000000
98! = 9426890448883247745626185743057242473809693764078951663494238777294707070023223798882976159207729119823605850588608460429412647567360000000000000000000000
99! = 933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000
100! = 9.33262154439441e+157

FAQ

How many Zeros are there in 100 factorial?

24

What is the number of digits in 100 factorial?

The number of digits in 100 factorial is 158.

What is the highest factorial?

Well, it’s actually undefined. We don’t know what the highest factorial is. However, we do know that factorial grows exponentially. That means that the higher the number, the faster it grows. And, since factorial grows exponentially, then the answer to our question is infinite.

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