Determine the number of zeros at the end of 3000!
Answers
➥ The number of trailing 0s in 3000! is 748
➥ The number of digits in 3000 factorial is 9131.
➥ The factorial of 3000 is calculated as below:
3000! = 3000 • 2999 • 2998 • 2997 • 2996 ... 3 • 2 • 1
Answer:
The number of zeros is 748
Step-by-step explanation:
Number of zeros at the end of a
Problem Type: Number of zeros at the end of p!
To solve such type of problem we see only a pair of 2 x5 in p! .
Because if a number is divisible by 10 then it will have 0 in the end and 10= 2×5 so finding the number of zeros is equivalent to finding the maximum power of 10 in p! which is the same as counting the number of pairs of 2 and 5.
3000! is exactly: 414935960343785408555686709308661217095111919493180991768946765769755856512353195008600076521780034200751846353836171184957508711140459077945534021610683396116210379041991775220626633901796828051647196974959688424577287660971030037261110953402411271188331577388153284389297376130211063129303744014853787254460796102904294910497938881207625116251329170046416689621175902035751754889806535778689152850937824699946746991908320935110683638242870635222685443392137751504885881040368188090992929124971419005089389944047153514731545315874415099601742678750874603679741170723687472771439889206836916185036081984597180937844535239585053776110865111623631459208861085574508745139453054362137118981508471920944263742032750299963337849440147756714146808242074999147148783596697206389546705899601785694802633887671128710680049508274007171248194763864013691935443541203127866014347925499591435301206531034066255032310207383515021951031486736123387393950965514621593490157899499440723110044269248381401414554878727380458560235615832043179459530558306933512468907212461514684853087240312679670891135489827334753757568993651763964247817334625108790157434373989204922670983170339321071763439833524445760404765654004144146994799843545545977993867028394285134131889131656953108485135250940061477740470073314065417944280044366919036854692708572717016480115120574524486079687737848036606530091098156390912941106337156215409038001350586716242623339024341666287165212285902745688335048979268693697928783768948414365738664369550754739648822562221833800146007611968592176032348084674552163304117380043311442259262436905587829149079738857587845857398286953903023838372658824276543064375177578972150450713618017300516284244762942274857556278287634987671952813689135839188244992847415916831303340321999467520829148857643458638323135452050759559120620672732969513861229946586075273178844524498653481641692388448890614958509343734428898148844273218171312725338915345065811438233812058753798086050808897617538828962529336337504545491686002672295912255288545844826866553243130113537548124095612376860780077007079395418489071494673778544075283078729881039129451219298647937034512574364455814597571408227059863251653529065845711235852702119334529811055683988098840949803461850780252730387367840421694272379804643042500450308066370327600163419214428057088024308505678921086469774551395391198386361671903002781463801369324823327715951805961930695042378360826205708872092979297974294045768773383198774446855442948003217410566894237105450288704196119150727390000316420144742133232938716180295556140046028674004228853898546503280284285151222960287957418016218232360983209714410470125330673148961532367887349845539496043970503523477662113959145192704221222314269986920874635209806862243548133761943951319428681134865315622281732149764817053818461553265961875302964786011608722636404439222576019264946109168851510131439455743983031925571541621514424691223705191490978618494361509631099336395945617965933968519586053386311763241470668422571923947425317264795597499932832472798078964707530540141940902006097126747531863655254032127577578539306975300565952082074574994718981444537722482078884433351185456015688537081828928952183001396543769472864187766657628153897373401594105436814354373461342446920670700827824236455574508825566701572427528103171416406314106813843309240272813189608848130406652261695528256371838624649442956888593938467267236941994755713205460182634257310291153535327288081827730215967870884372934121170845115806299676972666016636352769599690215021221049542595672785931855162684471003744346204220035353912037383930954206950214862073906531909108213443342514978962842361985716747738481260974430550362508663547207309712980846971965377227798931602005607250580075124074944481633922143981184927482819786551784785477491987141384850422903839540905708420381372771356677035650410817805206950321362335216......
The number of trailing zeros in 3000! is 748.
The number of digits in 3000 factorial is 9131.
The factorial of 3000 is calculated, through its definition, this way:
3000! = 3000 • 2999 • 2998 • 2997 • 2996 ... 3 • 2 • 1