Visualizing the 100 first factorials

100!
First find some definitions:

In[]:=
What is a factorial?
»
factorial
WORD
In[]:=
factorial
WORD
["Definitions"]//Column
Out[]=
{factorial,Noun}the product of all the integers up to and including a given integer
{factorial,Adjective}of or relating to factorials
In[]:=
WikipediaData["Factorial"]//TextCell[StringTake[#,700],"Text"]&
Out[]=
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n:​For example,​The value of 0! is 1, according to the convention for an empty product.The factorial operation is encountered in many areas of mathematics, notably in combinatorics, algebra, and mathematical analysis. Its most basic use counts the possible distinct sequences – the permutations – of n distinct objects: there are n!.The factorial function can also be extended to non-integer arguments while retaining its most important properties by defining x! = Γ(x + 1), where Γ is the gamma function; this is undefined when x is a negative integer.​​== Hi
Factorial function in Wolfram Language:
In[]:=
?Factorial
Out[]=
Symbol
n! gives the factorial of n.
Testing it
In[]:=
2!
Out[]=
2
In[]:=
5!
Out[]=
120
In[]:=
10!
Out[]=
3628800
View the 100 first factorials:
In[]:=
Table[n!,{n,0,100}]
Out[]=
{1,1,2,6,24,120,720,5040,40320,362880,3628800,39916800,479001600,6227020800,87178291200,1307674368000,20922789888000,355687428096000,6402373705728000,121645100408832000,2432902008176640000,51090942171709440000,1124000727777607680000,25852016738884976640000,620448401733239439360000,15511210043330985984000000,403291461126605635584000000,10888869450418352160768000000,304888344611713860501504000000,8841761993739701954543616000000,265252859812191058636308480000000,8222838654177922817725562880000000,263130836933693530167218012160000000,8683317618811886495518194401280000000,295232799039604140847618609643520000000,10333147966386144929666651337523200000000,371993326789901217467999448150835200000000,13763753091226345046315979581580902400000000,523022617466601111760007224100074291200000000,20397882081197443358640281739902897356800000000,815915283247897734345611269596115894272000000000,33452526613163807108170062053440751665152000000000,1405006117752879898543142606244511569936384000000000,60415263063373835637355132068513997507264512000000000,2658271574788448768043625811014615890319638528000000000,119622220865480194561963161495657715064383733760000000000,5502622159812088949850305428800254892961651752960000000000,258623241511168180642964355153611979969197632389120000000000,12413915592536072670862289047373375038521486354677760000000000,608281864034267560872252163321295376887552831379210240000000000,30414093201713378043612608166064768844377641568960512000000000000,1551118753287382280224243016469303211063259720016986112000000000000,80658175170943878571660636856403766975289505440883277824000000000000,4274883284060025564298013753389399649690343788366813724672000000000000,230843697339241380472092742683027581083278564571807941132288000000000000,12696403353658275925965100847566516959580321051449436762275840000000000000,710998587804863451854045647463724949736497978881168458687447040000000000000,40526919504877216755680601905432322134980384796226602145184481280000000000000,2350561331282878571829474910515074683828862318181142924420699914240000000000000,138683118545689835737939019720389406345902876772687432540821294940160000000000000,8320987112741390144276341183223364380754172606361245952449277696409600000000000000,507580213877224798800856812176625227226004528988036003099405939480985600000000000000,31469973260387937525653122354950764088012280797258232192163168247821107200000000000000,1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000,126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000,8247650592082470666723170306785496252186258551345437492922123134388955774976000000000000000,544344939077443064003729240247842752644293064388798874532860126869671081148416000000000000000,36471110918188685288249859096605464427167635314049524593701628500267962436943872000000000000000,2480035542436830599600990418569171581047399201355367672371710738018221445712183296000000000000000,171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000,11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000,850478588567862317521167644239926010288584608120796235886430763388588680378079017697280000000000000000,61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000,4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000000,330788544151938641225953028221253782145683251820934971170611926835411235700971565459250872320000000000000000,24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000,1885494701666050254987932260861146558230394535379329335672487982961844043495537923117729972224000000000000000000,145183092028285869634070784086308284983740379224208358846781574688061991349156420080065207861248000000000000000000,11324281178206297831457521158732046228731749579488251990048962825668835325234200766245086213177344000000000000000000,894618213078297528685144171539831652069808216779571907213868063227837990693501860533361810841010176000000000000000000,71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000,5797126020747367985879734231578109105412357244731625958745865049716390179693892056256184534249745940480000000000000000000,475364333701284174842138206989404946643813294067993328617160934076743994734899148613007131808479167119360000000000000000000,39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000,3314240134565353266999387579130131288000666286242049487118846032383059131291716864129885722968716753156177920000000000000000000,281710411438055027694947944226061159480056634330574206405101912752560026159795933451040286452340924018275123200000000000000000000,24227095383672732381765523203441259715284870552429381750838764496720162249742450276789464634901319465571660595200000000000000000000,2107757298379527717213600518699389595229783738061356212322972511214654115727593174080683423236414793504734471782400000000000000000000,185482642257398439114796845645546284380220968949399346684421580986889562184028199319100141244804501828416633516851200000000000000000000,16507955160908461081216919262453619309839666236496541854913520707833171034378509739399912570787600662729080382999756800000000000000000000,1485715964481761497309522733620825737885569961284688766942216863704985393094065876545992131370884059645617234469978112000000000000000000000,135200152767840296255166568759495142147586866476906677791741734597153670771559994765685283954750449427751168336768008192000000000000000000000,12438414054641307255475324325873553077577991715875414356840239582938137710983519518443046123837041347353107486982656753664000000000000000000000,1156772507081641574759205162306240436214753229576413535186142281213246807121467315215203289516844845303838996289387078090752000000000000000000000,108736615665674308027365285256786601004186803580182872307497374434045199869417927630229109214583415458560865651202385340530688000000000000000000000,10329978488239059262599702099394727095397746340117372869212250571234293987594703124871765375385424468563282236864226607350415360000000000000000000000,991677934870949689209571401541893801158183648651267795444376054838492222809091499987689476037000748982075094738965754305639874560000000000000000000000,96192759682482119853328425949563698712343813919172976158104477319333745612481875498805879175589072651261284189679678167647067832320000000000000000000000,9426890448883247745626185743057242473809693764078951663494238777294707070023223798882976159207729119823605850588608460429412647567360000000000000000000000,933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000,93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000}
How many digits has the max 100 first factorials?
In[]:=
Max[Table[n!,{n,0,100}]]​​DigitCount[%]
Out[]=
93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
Out[]=
{15,19,10,10,14,19,7,14,20,30}
This is the same as:
Integer length:
View 100! digits in a pie chart:
View the graph of the factorials integers...
Histogram of the factorial integers:
View the values in a bar chart:
View the values in a log bar chart:
Visualize the integer values in gray levels and colored:
Visualize the binary values in gray levels and colored:
Break down the 100! integer and view as a graph:
Put it all together with an interactive visualization, factorial integers graphs:
View as a centered text:
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