I have a time machine!

Number Theory Level 4

Find the last four non-zero digits in

2080 ! \large 2080!

Notation: 2080 ! = 1 × 2 × 3 × … × 2080 2080! = 1 \times 2 \times 3 \times \ldots \times 2080

Inspiration


The answer is 9184.

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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1 solution

Giorgos K.
Jan 3, 2018

19831399575419003738491318968613943828169802719685004480078302246591881170911040773634434711498083917544327251197967528166128837300761214988198621471487501365624868349812322280342508664016807589938954525597673546561445612029397867418592672670467332436974049047960817150889827779996732859071307850570918299387655093846244206737351742333363218958761602511342696995733646691846107530662081271559456083669981557780051181927018511838471452270920985350758549530444222275854497810649112857055868942318542316401197734707664863764917928045131308002810082480679178255968089024885457912604410076251400506127074083302477131169610561948912621647402513473323111910353783747289571756593622212412382339153721102940696466932609344547695824578341021057997500079133699861541847442474366356586256990835115287226040434778284247813565690425359745182123769623022491658386074158354782905376913410147338451819820986000870599148682506066958807519787860753974610505879887606870306040711026698285734752378948849271339695185598094816297145783314215853191849080701331322762930899467565568215144584166095280664271834592818058576489936334432326582212396197396232568320514451508816119196980179634050971863692345769107614274756835194051594330066742859335392508136180043741093553950578955411864817727802085156508884911985050545664395182647861082399869931227299246849494452821341347775357799250631372471909612978619835744098938519570467452651840728965181862958595873907667433905560879662545242428136719100601514134590279479301204551553827295430892877043771462672060397156327245561373343523261118853158672170021177098208765873417747280992276174421495910792087922867738380532628528347004050817082536981674354249883620024643086638640790934085533927931821812734902720972244193049856059418522903295606427028587797561754797335203902472201909002839571358218632568236864084286262553682794806170194615406720172960226684411602102004074405262231622886485314681347988959803406324570213060317454405071926921948746285329949122555107753998414179251928015695736204686523918791509369181274611024932572672687366199710359410351601554526384415364602998358869176162026432723744752609482891748538246849921411368580858673745233984972816957770787688199040940586269769758659100842027452872480450188413488147732664880712807544377145440995910283273351627028770376104138358773783183771677868356742057644158204049043183240662434043751974000598252022091627764069535765682125596261549502284235837698233140625782281996128411336938911055562440472227119752818846439953460436309373810753873224981926305964786000941370872420569276967759280885039770839557557842964239149422132391615035154447971758071215606845249130076952514164829306750146949838278385455284559183951199233189767672337423258473461889054615285108366805548473100256083260129955728282863630271801348043813943936018282470589005754815786170068101312809107903424064452735198182657440154570270652210683717722029962904811725454419994421266850676921256032270577775609570735014817912530582474756919137031910010545276069433868793234366281428259027664380266173061139228991623896048838438965765319156477829272112419776831313436207670711433861214572799596456385652708979161338250001570046099601280690641314300023867320005783197696799710549070903090302699042957739678018035787815974436979982322304893913297351193512421704120404055333013688884064330758784672304680009670895529836790219928889196995639372380514248247466929215927588916175499684941210307010955982082658102426804138816771231398214762362998672666751656212586221221684798267428309758103455946000025028364976797037045079891015079773499015513624154844837782494392620290588867451005848380216254263813864428008136117818268296249347182869607834620514796861441206573810171846516542463170741329095776414276717575073408651022282668602256925092763013866582482141171530763905414529746395301084063641539157644452409241408045091473337473875828142832028702031781638019409961676289130536173842045153503504912813903496910909697505720030724856348936657308375846703500969066947633319545508776893759981218559988074171277039989589481778791260431648461951752806802214227202477771683127241058281307768065067539856648092610823504840537033802051120191646372165101550848246185294834385819426352290210351747332694765620286698033671455469549153978594560007675569632818443333967878516902063777932137968305489547458948100164273848723538521775803605502737854170843507814908034834270216965075381861706259466736880283700989459340386730157207726294307862759440941151037785635335131414554735764090155218401002079943363930151748272899601315622005062291008632805456504269801179315365154163530271639335451680665123727208851814159961865159810240849157641389042998810431278850835613000176530780448184290906690693760810602019230177066410934872989130962448633372453419294426954779568458787690617141993744898950880446213838942698151319070085238941811911026595948350306149541797550278808203006150815756711333114747481707282477168427766286835062787668330306061801743153029592046115296149742224628597884058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