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Question

what will be the units digit of 2^31921???

and why/how did u get that?

Answer 1

As the value of the power increases, the units digit is in the sequence 2 4 8 6, with 4 terms.
So divide 31921/4, and you get a remainder of 1, so the answer is 2.

Answer 2

2^31921 =
150831340196443155686031676128 289387302370588493593234373037 863407929050156376183707812267 292726120482939994338197592581 806460322102292162387401541522 541092467107928675340912376943 536318799990888086439767771611 340343905644715679943948877289 127510116312875697528845331034 525012715015703628149026946755 151592091212989996180180019516 463609600942380005376206180620 635751980958336346957393363493 641667165236207488155785664608 743712837388957904708840608132 492152638074629654406517808457 533344324380138711158946022879 213568156624981494259002702826 638525166769360887146228450437 827162170287796827313315555703 957561154989062834794674993922 068267152109739275829098366293 234035233247581398175193379870 956662999076866471829113982467 732809770141167270890518796412 392641303844322534263573855085 503077771274360938783226757420 165161515847952941266186744503 174581721524592751812333757458 622409260197103898761175977303 474532508366355915351453582181 549017647328846249139085182996 491257254786506491386374706111 015072294620724352277706170843 664782013926225608282082429701 705901955054205647418136404565 542974679272145938764263541851 980585757603303965641136452921 756513113318779300001115846477 500084228274222882258425829850 476011238717384332722903761829 036860719676340491042679890306 707553910963484448615178824976 302603041306564496998213863751 262797154531933540562981887663 716599011025443371514328274581 131289450481958277108352936734 806086110867553691812045381431 128876376421153719224948923863 511724314799064648399380608536 812143378719735539051159875559 638351677613535039127209184569 222083239520989269099917753830 249599843600953505985248896451 314964664386973791016672536032 378013135452133259184452518571 565578338360510520635006159263 584335237485419767918112183670 540716034596954505779413265331 021334617047637339747132899790 704284873486548791578687870083 558008550140932614066344913845 069593109000725236891438747168 364108281110342203878377037352 625667072617984691385850913979 255409068240309571965129102456 929531849483153926171671680741 801900953307605152417348725957 060677334831374835517859917472 439269667967801050530820019960 491814632856592647497813071502 692894773369701711852422584398 814106726989282525440353304839 601126391216567453184468883982 689519150508019542770269279454 836058407389960716094843569297 986335258105867681937795694198 299950814470932718853865152178 452737123135170820747462958213 775642325304458030212284892032 287529081111715018737436090224 657080450168675088089585197950 302947240232214273572319033177 700818653263353419542162370761 408656051647934080295579290616 622069206258669566972312546574 621932554784519232300609302183 025617232300993666114285986209 942781880312642841277639695997 211086579341047791718386717378 417712842170998547204879508937 085744824940536994158946949423 914924810210947234504848771359 192000937711987602616951604202 089350680316090148992134939529 836051843397734635238721735340 983299146586417429049012850389 375659096901612702314369538144 645216605632197033787438437366 945573843603881283793847653639 801281856386396196386600769161 074065886659853540863586472583 168853394165292950210016360978 382555158741168467756247640896 547543650528031941173178404816 903569971438003752323110885682 387440027825239781776759201460 836805344890631178476320717068 166452754548022732567975610994 146515610747557091421829642431 095358697082762533569139198794 957373521994424898318246728359 894381176533105223609164470819 249303346167058333505227320902 641901013320240957672676195734 651019246572898839662615114263 948531863905955345858229189401 297894437084964627962984656642 876964021312375019458705160755 903114889662486702995232637396 698407158022048839222167940325 244912819592484872923822319180 180173710240418681026474406923 128084271227070836882525711785 540472515567601975483267192674 265728468039756942669128412058 732167597164075149550518015222 305011164355462708840729397176 479077269753478418569550565859 485327622814050891722054492276 658207448030571390852891133133 343109289040841085904312643510 093442828795052896488562398982 292372499819511277406123781657 209925213342069585543185064040 679474971465700431596034936905 593596913315599128600052768826 837240678377990652675147162742 274498870610009132424826717293 043820508833894562706177542653 369704819766470387910736469309 573942093769385130692874633307 748032220694621417121566965525 801817029649741414390448257522 139785462675523796933194790251 983787091479225906591385665784 160002292678774028823320087198 191910947856362289456595162374 712540173249995206111267020202 526421090737057342135059271005 122325455180105043989002671827 178049239532961508394352029184 937121280666804986626174041726 619200902915071704372220019406 069266177416620553468404822201 930162693276880670488933642466 207876432015420076221103238167 713854943790051500013149871410 761704638170417426619620617412 945998588719248010075541496536 297510409439426907454515708216 685789598281195544121608289497 898502309310972162119227223235 338323063225006606384201678657 336375357189223598912342296957 077609308395602565839042542782 545484810861012758998534459861 144739791032710889268166669081 979472577499098558813602265357 539141646240988547322511191402 704369365370317060521091948062 670856572924687297966313748285 795104245583119476015744543163 495644906761579031011698757920 012613670828735528448559343461 575567047144343374291679412306 271147216367596029105837927684 424633491654274962585022015586 723088360222726820139039223347 669571832661070714606047054331 444853449924000760059452577906 782169881895797591216651226396 970224748105994333195987562554 217883846350252696906863864238 418499771091060138925740648664 917502185360092875344868483171 432529004997421373450087158440 349681453496474760649259447537 581358554290420759742885449104 575904215248614317395398437847 643740773207403504042161625824 034257038913983588298769778541 790805881067178657444065459618 841313473151778459285421924090 920234507760786268617731840890 425698240853648531898547344000 134461867861468824772176368175 642764250031914961415582670218 528671760038530871659210149091 965086602978676253565401360755 840928610669608184507465389747 906154186947539321899918283902 240599922346784701552152720483 821669724755630603123312228547 716684817146661844296289252265 714545702228619716672555930995 959353348481305011234763193564 295815303649659933831916046591 743372915271358075851685974858 028253785327293863626762164756 562930756402369446080828493643 181987721506749559674140689969 421686050800358226735031473755 915748353536413288846699820793 300333263009285560598486776253 639154085212792445641831756330 212880469482399555282576432966 050398880895499275443753760809 126276651382517455284374217326 785352834303724321336881597881 713144949911439564759921422729 013105541557117721858392002094 654714114269302717198642804248 967379905993262837413825104013 862152665099154260022492233158 442086177379520168799767117876 225889358147075047558160551390 530013168411588821961995568900 709227583239438856751225149117 856841978333424056264856917175 814400626662778797238866553457 915169817225002036357202534495 592728191068870419362048690270 440792328704599319640713367135 608792349523488781871083698926 229826665857784962494599867332 140783877042884714998744479572 004174459235365749993563859053 293563495539779352757258239406 423164869646644434339510507143 853697168841032352247645593398 971599839507490326481654338109 922256772998704950917217207676 302841118445363938755558913107 990452786936765363028291519644 605020589299468883653047068086 603741487176626573974642726713 992220109467535929782712472174 725195291677034728951593002907 915347143213908030486776510196 818114033419429971220832674591 281773250083525384142223316463 956288256609652962037761687438 225622764559977226386181758468 246325492903929950978045067231 798281314994393071341450988208 744738728853659093844810458371 607716763348995814480375315512 696968058119830667347260625207 825798926861704826175023046724 589920746958348760954659147058 751446763967894465303765722243 920767921338603732702336598614 423016579031209859358271718467 674191692315371368976608062156 150485179217264837588377166547 316839307046417136147751171098 158681399110650764124884754387 940464783983645361247908268451 040501974352299697107499418339 586872637401376938857121806318 230231877074941325722554975489 013682302444178012641362814608 825611958320604272432705753514 877367073413086009833053351233 312531759468011856891408495884 287318383479606258470877990691 809305079486908464220179669552 661486294436941819390703908202 504772672029225696235477755662 405352547792571716212657402698 155617881918823232791298566793 222698651019025149568549942470 897146137439126618639620241323 519943167796133328483642990833 484601547966511950253493244226 601946171905955104214449280535 188793658248868547333725953826 465625660899311345816097740775 458764268044835975719424071843 833739258773910844289057707472 999754100566765668496859415919 480255307809385699836420561407 865392740750376168556777266249 929520038325806389260344137615 058247422289740240109376722038 988920373508309937899439199085 390992586913757369059913038240 316471263653671174916843259301 810808275939015710392428496248 395894222140484314629165154968 582085444250270678484677397505 040666759960262591211167564203 494311271505197169990475100736 648687924435368088227986357809 856901041803332322232583212278 326488780566468797544601132655 768606590185321464511999477817 273562382233029731049394352742 324250184818086562147687894262 791353008362218111716901633628 041613241813033614873691831920 018331348001280189825077300224 361127054457938231314792988338 755732299881388652921106094322 176849458925457540285721608503 661227035008520399206713116491 337602300040188512754934561779 602321383412772713654661907431 471603505269829261208129268924
2064945152

(p.s. this number is correct. really. aazib_1 doesn't know what he's talking about. and it certainly isn't prime!)

Answer 3

the units digit is 2. Start to calculate powers of 2 and watch the units digit

Power of 2 Units digit
2^1 2
2^2 4
2^3 8
2^4 6
2^5 2
2^6 4
2^7 8
2^8 6
2^9 2

Do you see what's happening? The units digits column is repeating in cycles of length 4,

2486 2486 2...

If you continue this list for 31921 rows how many cycles of length 4 will there be? How many more rows are there after that? What is the units digit in the 31921th row?

Answer 4

Lets try to reason this somehow...

2^31921 = 2 * 2^32920 = 2* (2^10)^3192

2^10 = 1024. So, this will be a bit better, since the powers of 4, the unit digit of 1024, are 4 and 6 (4, 16, 64, 256, etc.)

Lets think now of

4^3192. Since its a even exponent, the unit digit will be 6.

But all of that was multiplied by a 2, so the last unit digit of this number will be a 2 (6*2 = 12)

Ana

Answer 5

The answer is 2, and here's how you solve it:

2 raised to any power will end with an even digit:

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128

etc.

As you can see, the digit value cycles through 2, 4, 8, 6 then repeats over and over.

So look at the pattern between the exponent and the units digit, as follows (first column is exponent, second column is units digit):

1 2
2 4
3 8
4 6
5 2
6 4
7 8
8 6

So you can see that the value of the units digit is based on modulo 4 counting of the exponent. In other words, let X = exponent, and you can say that:

When x(mod4) = 1, the units digit = 2
When x(mod4) = 2, the units digit = 4
When x(mod4) = 3, the units digit = 8
When x(mod4) = 0, the units digit = 6

So look at 31921 divided by 4:

31921/4 = 7980 with remainder of 1

So 31921(mod4) = 1

Therefore the units digit of 2^31921 will be 2.

Hope that helps! And I hope that the explanation made sense for your grade level! :-)

Answer 6

Hey you put this question and then withdrew it.

To answer to your question, the answer is Infinity.

No human, computer or a calculator can calculate to get an answer.

On top of that this number seems to be a prime number, else I would have tried to break it up and reply back to your question.

Answer 7

1,018,950,241
this is the square root of 31921.
hope this helps! good luck!! :)