2007-11-29 15:01:22 · 4 answers · asked by Answer Seeker 1 in Science & Mathematics ➔ Mathematics
00. Your expression has at least two factors of 5 and at least two factors of 2; that's two factors of ten which forces the last two digits to be zero.
2007-11-29 15:04:33 · answer #1 · answered by jgoulden 7 · 1⤊ 0⤋
The last 500 digits are zero.
The number of trailing zeros will be the number of factors of 10 in 2006!, and that will be the number of factors of 5. (There are many more factors of 2)
There are 500 factors of 5 in 2006!
= int(2006/5) + int(2005/25) + int(2006/125)
+ int(2006/625) = 401 + 80 + 16 + 3
= 500
By the way,
2006! =
214479447870477983562897335854 616875534162652542603410252619 466560306311203490198782670768 588598261126473608326530650383 544231271859879097709523836937 367502641635780580693698694877 573097159986606404577178894503 340289200052117918299437518225 088573113945554825701815376266 861815939107944848264937329744 296633125806653714767848619051 478180453724438196214050142995 615623525752857633360085903949 494337147230721082450809620660 632722071965231854823459266747 728864521577256548461339202981 300288141351675051775738360220 009507273249290558631133401747 964625228496085026400607027040 228532719366440600359590873411 097356857303809970492017969613 689859976417274189188675626319 064118281488362914076360722298 698805572637864515292087489114 067369677431290546463788341289 616388805773475300569868045350 637351919242029267597166576516 938064916270707672165036906579 527842423648165618883377821889 062071082529656532380797546103 533081665382181151927912283479 487648254588516952588314103860 846149348488393484305710929540 144884159032072551211541439760 139121463155437619176583216700 714258784472169294635199602186 847724901825346846883049643650 381360100569261352393475585537 358126966689074769297773409000 323078482329204827781419633581 721406989480722463745554818165 465840942359053327247882994076 613490430275399118485811969726 191355093736892192612699235796 631386644038144992296631302206 438749356958535796784971466776 408847850814494401504066633225 104372283287990324397369621580 833881149664646993790504299486 499175422799783908580949014098 236109805789141039829743225032 570502776816509405822423624022 242731939364160330380058685155 499794387452163850187155561514 234354617596580126400981868144 659290949949433103381240932149 172591479995750938306609119255 960201365367232765805830742130 492484095868494497249918131548 442370072894527733195527276241 924244159212562320623764270241 888111839126548700678564458237 189330007362074551633928613673 113014039116390922110562303055 503050713439247931260329250410 327127257518083819791213634933 426663387571130269017419363985 040467507374861609820351732888 623491970712958426676515219454 871280424225669985778082780662 651602332453061282895414471091 175070656123096383641240497777 122349464167905261781695030965 323421997378992591369907697594 705179918075503314501043235365 875575524714028149796067454179 511774321987400432787265335366 210880852477850936164745846696 604656394121102745051838195286 852578471311226746253378226326 144282381436271336060466991787 727106577710809429407557952187 562032579239811556179978348254 322102965631007855291360892510 426356131448315093402688705672 935963822768354713332439154961 502094877971080555151721088742 378743333196268228747148832025 783155620215262563520364666584 111262780050468765175069817396 376622561287829962266376986065 887574755960620677010231929101 941430347763859901354103537416 647912703015956112964831137136 887943950912594742507273139482 567082481379867609346706881232 778189376871632066930706853403 187600031970431741460092989630 403878746390755386245145389545 581906340445599830837242985678 829177224960367538446220142311 341167869120318622305154890478 365624220812566421684213021529 176363283752280447657037771998 780459776669104178498884244402 385995936353635515168070602231 394449946531666222420777055972 155231679786903613382010541714 184617481820627901897318924112 128193750615959852969666945682 637609654480817615071726373663 961286898396817584503237759183 819967486505615916574780945358 505062214063333989830919201474 425519785240224508938590092311 225027505880611401745874628125 003604611850041417268652143211 871016679282528899571889012611 206724181170358010282056125336 072100229492542410936485382954 060632214696306615080330069963 758571483955190505824278142430 786621238398594465737627887078 882406538204087876424908159346 074911778313946395236415401363 160857331031217109107360382462 713261951263305834832136098677 447894169000125097160308032782 572788896811828283294723773657 021873598515743245352845602047 966235694238194149010974508382 270190556925421496367133232593 796993927147947397329651663226 424181354998427155987344879143 210259365323860493172192565126 592411845521068219591006666723 781940639266418747222670799751 523471961502542701422345110155 059167165121757338856250933295 033873989762492818972623969966 632391566450716064040751088969 415122679492720785798283893650 773099790015728056168502880379 976508365771410891255503423595 118144404449033585367675692106 403526879105733960566480548176 749160905397175953991337622033 055891502792531358305328946372 833821112445744768731595328927 843040661248898021095864184437 336068582150786038629826823523 983962553229601941773918703614 924509043003209264871859776769 097676505938037992247311830671 004139283695469768850806258395 194553252552778291154795467946 113039059992921311897039830045 645245514420018426378258378241 194072469725165665991896409755 305768003249006175462913381773 369690656360006709465824009199 553417902350934559393706225643 560886637957793720414001577167 233355314246455494255139587429 352912249588967670782309015805 951178637829848560947223529720 260349456655471527746535541404 797488775756258646314649568478 398656293546312778343031980774 630118948291636950488763776619 861115578716405567892513981096 697070585773541941779997788336 861270421132632012384005944498 458176569013308269344900004200 439244488516250770212849410927 230976000000000000000000000000 000000000000000000000000000000 000000000000000000000000000000 000000000000000000000000000000 000000000000000000000000000000 000000000000000000000000000000 000000000000000000000000000000 000000000000000000000000000000 000000000000000000000000000000 000000000000000000000000000000 000000000000000000000000000000 000000000000000000000000000000 000000000000000000000000000000 000000000000000000000000000000 000000000000000000000000000000 000000000000000000000000000000 00000000000000000000000000
exactly.
=
2^1998 * 3^998 * 5^500 * 7^331 * 11^199 * 13^165 * 17^124 * 19^110 * 23^90 * 29^71 * 31^66 * 37^55 * 41^49 * 43^47 * 47^42 * 53^37 * 59^34 * 61^32 * 67^29 * 71^28 * 73^27 * 79^25 * 83^24 * 89^22 * 97^20 * 101^19 * 103^19 * 107^18 * 109^18 * 113^17 * 127^15 * 131^15 * 137^14 * 139^14 * 149^13 * 151^13 * 157^12 * 163^12 * 167^12 * 173^11 * 179^11 * 181^11 * 191^10 * 193^10 * 197^10 * 199^10 * 211^9 * 223^8 * 227^8 * 229^8 * 233^8 * 239^8 * 241^8 * 251^7 * 257^7 * 263^7 * 269^7 * 271^7 * 277^7 * 281^7 * 283^7 * 293^6 * 307^6 * 311^6 * 313^6 * 317^6 * 331^6 * 337^5 * 347^5 * 349^5 * 353^5 * 359^5 * 367^5 * 373^5 * 379^5 * 383^5 * 389^5 * 397^5 * 401^5 * 409^4 * 419^4 * 421^4 * 431^4 * 433^4 * 439^4 * 443^4 * 449^4 * 457^4 * 461^4 * 463^4 * 467^4 * 479^4 * 487^4 * 491^4 * 499^4 * 503^3 * 509^3 * 521^3 * 523^3 * 541^3 * 547^3 * 557^3 * 563^3 * 569^3 * 571^3 * 577^3 * 587^3 * 593^3 * 599^3 * 601^3 * 607^3 * 613^3 * 617^3 * 619^3 * 631^3 * 641^3 * 643^3 * 647^3 * 653^3 * 659^3 * 661^3 * 673^2 * 677^2 * 683^2 * 691^2 * 701^2 * 709^2 * 719^2 * 727^2 * 733^2 * 739^2 * 743^2 * 751^2 * 757^2 * 761^2 * 769^2 * 773^2 * 787^2 * 797^2 * 809^2 * 811^2 * 821^2 * 823^2 * 827^2 * 829^2 * 839^2 * 853^2 * 857^2 * 859^2 * 863^2 * 877^2 * 881^2 * 883^2 * 887^2 * 907^2 * 911^2 * 919^2 * 929^2 * 937^2 * 941^2 * 947^2 * 953^2 * 967^2 * 971^2 * 977^2 * 983^2 * 991^2 * 997^2 * 1009 * 1013 * 1019 * 1021 * 1031 * 1033 * 1039 * 1049 * 1051 * 1061 * 1063 * 1069 * 1087 * 1091 * 1093 * 1097 * 1103 * 1109 * 1117 * 1123 * 1129 * 1151 * 1153 * 1163 * 1171 * 1181 * 1187 * 1193 * 1201 * 1213 * 1217 * 1223 * 1229 * 1231 * 1237 * 1249 * 1259 * 1277 * 1279 * 1283 * 1289 * 1291 * 1297 * 1301 * 1303 * 1307 * 1319 * 1321 * 1327 * 1361 * 1367 * 1373 * 1381 * 1399 * 1409 * 1423 * 1427 * 1429 * 1433 * 1439 * 1447 * 1451 * 1453 * 1459 * 1471 * 1481 * 1483 * 1487 * 1489 * 1493 * 1499 * 1511 * 1523 * 1531 * 1543 * 1549 * 1553 * 1559 * 1567 * 1571 * 1579 * 1583 * 1597 * 1601 * 1607 * 1609 * 1613 * 1619 * 1621 * 1627 * 1637 * 1657 * 1663 * 1667 * 1669 * 1693 * 1697 * 1699 * 1709 * 1721 * 1723 * 1733 * 1741 * 1747 * 1753 * 1759 * 1777 * 1783 * 1787 * 1789 * 1801 * 1811 * 1823 * 1831 * 1847 * 1861 * 1867 * 1871 * 1873 * 1877 * 1879 * 1889 * 1901 * 1907 * 1913 * 1931 * 1933 * 1949 * 1951 * 1973 * 1979 * 1987 * 1993 * 1997 * 1999 * 2003
2007-11-29 23:13:52 · answer #2 · answered by Scott R 6 · 1⤊ 0⤋
combination of 5 and 2 makes one zero. The above product has many (5*2)..... so the answer for the above question is 00
5*2 = 10
5^2 * 2^2= 10^2= 100
5^3 * 2^3= 10^3 = 1000
1x2x3x4x5x.....x10 => last two digits are 00
1x2x3x4x5x.....x100 => last two digits are 00
1x2x3x4x5x.....x2005x2006 =>last two digits are 00
2007-11-29 23:20:04 · answer #3 · answered by prabhu 1 · 0⤊ 0⤋
zero
ok thanks
2007-11-29 23:30:17 · answer #4 · answered by sanjeewa 4 · 0⤊ 0⤋