12513603929656774877900
12,513,603,929,656,774,877,900 is an even composite number composed of six prime numbers multiplied together.
What does the number 12513603929656774877900 look like?
This visualization shows the relationship between its 6 prime factors (large circles) and 1620 divisors.
12513603929656774877900 is an even composite number. It is composed of six distinct prime numbers multiplied together. It has a total of one thousand, six hundred twenty divisors.
Prime factorization of 12513603929656774877900:
22 × 52 × 113 × 174 × 612 × 173932
(2 × 2 × 5 × 5 × 11 × 11 × 11 × 17 × 17 × 17 × 17 × 61 × 61 × 17393 × 17393)See below for interesting mathematical facts about the number 12513603929656774877900 from the Numbermatics database.
Names of 12513603929656774877900
- Cardinal: 12513603929656774877900 can be written as Twelve sextillion, five hundred thirteen quintillion, six hundred three quadrillion, nine hundred twenty-nine trillion, six hundred fifty-six billion, seven hundred seventy-four million, eight hundred seventy-seven thousand, nine hundred.
Scientific notation
- Scientific notation: 1.25136039296567748779 × 1022
Factors of 12513603929656774877900
Divisors of 12513603929656774877900
- Number of divisors d(n): 1620
-
Complete list of divisors:
1 2 4 5 10 11 17 20 22 25 34 44 50 55 61 68 85 100 110 121 122 170 187 220 242 244 275 289 305 340 374 425 484 550 578 605 610 671 748 850 935 1037 1100 1156 1210 1220 1331 1342 1445 1525 1700 1870 2057 2074 2420 2662 2684 2890 3025 3050 3179 3355 3721 3740 4114 4148 4675 4913 5185 5324 5780 6050 6100 6358 6655 6710 7225 7381 7442 8228 9350 9826 10285 10370 11407 12100 12716 13310 13420 14450 14762 14884 15895 16775 17393 17629 18605 18700 19652 20570 20740 22627 22814 24565 25925 26620 28900 29524 31790 33275 33550 34786 34969 35258 36905 37210 40931 41140 45254 45628 49130 51425 51850 54043 57035 63257 63580 66550 67100 69572 69938 70516 73810 74420 79475 81191 81862 83521 86965 88145 90508 93025 98260 102850 103700 108086 113135 114070 122825 125477 126514 133100 139876 147620 158950 162382 163724 167042 173930 174845 176290 184525 186050 191323 193919 204655 205700 216172 226270 228140 245650 250954 253028 270215 285175 295681 299693 316285 317900 324764 334084 347860 349690 352580 369050 372100 382646 384659 387838 405955 409310 417605 434825 440725 450241 452540 491300 501908 540430 565675 570350 591362 594473 599386 627385 632570 695827 699380 738100 765292 769318 775676 811910 818620 835210 869650 874225 881450 900482 918731 956615 969595 1023275 1060973 1075369 1080860 1131350 1140700 1182724 1188946 1198772 1254770 1265140 1351075 1380247 1391654 1478405 1498465 1538636 1581425 1623820 1670420 1739300 1748450 1762900 1800964 1837462 1913230 1923295 1939190 2029775 2046550 2088025 2104553 2121946 2133109 2150738 2251205 2262700 2377892 2509540 2702150 2760494 2783308 2956810 2972365 2996930 3136925 3162850 3252491 3296623 3479135 3496900 3674924 3826460 3846590 3878380 4059550 4093100 4176050 4209106 4243892 4266218 4301476 4502410 4593655 4783075 4847975 4952651 5026577 5094781 5304865 5376845 5404300 5520988 5913620 5944730 5993860 6273850 6325700 6504982 6539203 6593246 6901235 6958270 7392025 7492325 7654097 7693180 8119100 8352100 8418212 8532436 9004820 9187310 9566150 9616475 9695950 9905302 10053154 10106041 10189562 10522765 10609730 10665545 10753690 11256025 11670703 11829059 11889460 12547700 13009964 13078406 13186492 13802470 13916540 14784050 14861825 14984650 15308194 16262455 16483115 17395675 18036541 18281273 18374620 19132300 19232950 19391900 19810604 20106308 20212082 20379124 21045530 21219460 21331090 21507380 22512050 22968275 23150083 23341406 23464199 23658118 24763255 25132885 25473905 26156812 26524325 26884225 27604940 29568100 29723650 29969300 30616388 32524910 32696015 32966230 34506175 34791350 35777401 36073082 36262853 36562546 38270485 38465900 40424164 42091060 42662180 45024100 45936550 46300166 46682812 46928398 47316236 49526510 50265770 50530205 50947810 52613825 53048650 53327725 53768450 55292347 56042591 58353515 59145295 59447300 64719353 65049820 65392030 65932460 69012350 69582700 71554802 72146164 72525706 73125092 76540970 81312275 82415575 84195067 85451809 90182705 91406365 91873100 92600332 93856796 99053020 100531540 101060410 101895620 105227650 106097300 106655450 107536900 110584694 111166451 112085182 115750415 116707030 117320995 118290590 123816275 125664425 127369525 128377733 129438706 130119649 130784060 138024700 143109604 145051412 153081940 162624550 163480075 164831150 168390134 170903618 178887005 180365410 181314265 182812730 191352425 198401951 201094003 202120820 210455300 213310900 221169388 222332902 224170364 231500830 233414060 234641990 236581180 247632550 251328850 252651025 254739050 256755466 258877412 260239298 276461735 280212955 291767575 295726475 302516449 306621197 310781641 323596765 325249100 326960150 329662300 336780268 341807236 357774010 360730820 362628530 365625460 382704850 393551411 396803902 398891383 402188006 420975335 427259045 444665804 450913525 457031825 463001660 469283980 495265100 502657700 505302050 509478100 513510932 520478596 552923470 555832255 560425910 578752075 583535150 586604975 591452950 605032898 608215817 613242394 616468501 621563282 641888665 647193530 650598245 653920300 711912883 715548020 725257060 765409700 787102822 793607804 797782766 804376012 841950670 854518090 894435025 901827050 906571325 914063650 939969899 992009755 1005470015 1010604100 1100229001 1105846940 1111664510 1120851820 1157504150 1167070300 1173209950 1182905900 1210065796 1216431634 1226484788 1232937002 1243126564 1283777330 1294387060 1301196490 1382308675 1401064775 1412155063 1423825766 1431316139 1452680753 1512582245 1533105985 1553908205 1574205644 1595565532 1617983825 1683901340 1709036180 1788870050 1803654100 1813142650 1828127300 1879939798 1967757055 1984019510 1994456915 2010940030 2104876675 2136295225 2182421461 2200458002 2212034033 2223329020 2315008300 2346419900 2432863268 2465874004 2567554660 2602392980 2764617350 2779161275 2802129550 2824310126 2847651532 2862632278 2905361506 3025164490 3041079085 3066211970 3082342505 3107816410 3209443325 3235967650 3252991225 3327680939 3372833167 3418598051 3559564415 3577740100 3626285300 3759879596 3935514110 3968039020 3988913830 4021880060 4209753350 4272590450 4364842922 4400916004 4424068066 4699849495 4960048775 5027350075 5142779633 5212560349 5501145005 5529234700 5558322550 5604259100 5648620252 5725264556 5810723012 6050328980 6082158170 6132423940 6164685010 6215632820 6418886650 6471935300 6505982450 6655361878 6690373987 6745666334 6781153511 6837196102 7060775315 7119128830 7156580695 7263403765 7562911225 7665529925 7769541025 7831041713 7871028220 7977827660 8419506700 8545180900 8729685844 8848136132 9399698990 9838785275 9920097550 9972284575 10054700150 10285559266 10339668889 10425120698 10912107305 11002290010 11060170165 11116645100 12102519011 12164316340 12329370020 12837773300 13011964900 13310723756 13380747974 13491332668 13562307022 13674392204 14121550630 14238257660 14313161390 14526807530 15125822450 15205395425 15331059850 15411712525 15539082050 15662083426 15979488283 16638404695 16864165835 17092990255 17797822075 18453503389 18703893017 18799397980 19677570550 19840195100 19944569150 20109400300 20571118532 20679337778 20850241396 21824214610 22004580020 22120340330 23499247475 24006636071 24205038022 24332374363 25713898165 26062801745 26761495948 27124614044 27505725025 28243101260 28626322780 29053615060 30251644900 30410790850 30662119700 30823425050 31078164100 31324166852 31958976566 33276809390 33451869935 33728331670 33905767555 34185980510 35303876575 35595644150 35782903475 36317018825 36604490329 36907006778 37101164837 37407786034 37604578561 39155208565 39355141100 39889138300 41358675556 43648429220 44240680660 46998494950 48013272142 48410076044 48664748726 51427796330 51698344445 52125603490 54560536525 55011450050 55300850825 56570575963 57338163839 60512595055 60821581700 61646850100 63917953132 66553618780 66903739870 67456663340 67811535110 68371961020 70607753150 71191288300 71565806950 72634037650 73208980658 73814013556 74202329674 74815572068 75209157122 78310417130 79897441415 83192023475 84320829175 85464951275 86141458843 87427253761 88613525933 92267516945 93519465085 93996989900 96026544284 97329497452 102855592660 103396688890 104251206980 109121073050 110022900100 110601701650 113141151926 113736357779 114676327678 120033180355 121025190110 121661871815 128569490825 130314008725 133127709121 133807479740 135623070220 141215506300 143131613900 145268075300 146417961316 148404659348 150418314244 156620834260 159794882830 166384046950 167259349675 168641658350 169528837775 170929902550 172282917686 174854507522 175774371113 177227051866 183022451645 184535033890 185505824185 187038930170 188022892805 195776042825 202988537279 205742823187 206793377780 218242146100 221203403300 226282303852 227472715558 229352655356 240066360710 242050380220 243323743630 257138981650 258491722225 260628017450 266255418242 282852879815 286690819195 302562975275 313709557613 317966181289 319589765660 332768093900 334518699350 337283316700 339057675550 341859805100 344565835372 349709015044 351548742226 354454103732 366044903290 369070067780 371011648370 374077860340 376045785610 391552085650 399487207075 402649393619 405977074558 408112813207 411485646374 413650364171 430707294215 437136268805 443067629665 454945431116 461337584725 467597325425 480132721420 486647487260 514277963300 516983444450 521256034900 532510836484 565705759630 568681788895 573381638390 600165901775 605125950550 608309359075 622276335593 627419115226 630719802229 635932362578 665638545605 669037398700 678115351100 703097484452 732089806580 742023296740 752091571220 783104171300 798974414150 805298787238 811954149116 816225626414 822971292748 827300728342 861414588430 874272537610 878871855565 886135259330 915112258225 922675169450 927529120925 935194650850 940114464025 961699791371 974748785263 1014942686395 1028714115935 1033966888900 1125663706729 1131411519260 1137363577790 1146763276780 1200331803550 1210251901100 1216618718150 1244552671186 1254838230452 1261439604458 1271864725156 1331277091210 1414264399075 1433454095975 1464404800331 1486263313937 1568547788065 1589830906445 1597948828300 1610597574476 1632451252828 1654601456684 1722829176860 1748545075220 1757743711130 1772270518660 1830224516450 1845350338900 1855058241850 1870389301700 1880228928050 1923399582742 1933518082243 1949497570526 2013246968095 2029885372790 2040564066035 2057428231870 2068251820855 2153536471075 2185681344025 2215338148325 2232873910069 2251327413458 2263171055057 2274727155580 2400663607100 2433237436300 2489105342372 2522879208916 2662554182420 2828528798150 2843408944475 2866908191950 2928809600662 2972526627874 3111381677965 3137095576130 3153599011145 3179661812890 3328192728025 3450805133743 3497627994179 3515487422260 3660449032900 3710116483700 3760457856100 3846799165484 3867036164486 3898995141052 4026493936190 4059770745580 4081128132070 4114856463740 4136503641710 4307072942150 4371362688050 4394359277825 4430676296650 4465747820138 4502654826916 4526342110114 4808498956855 4873743926315 5074713431975 5143570579675 5333062479421 5405425081913 5628318533645 5657057596300 5686817888950 5733816383900 5857619201324 5945053255748 6222763355930 6274191152260 6307198022290 6359323625780 6656385456050 6845039691523 6901610267486 6937917824519 6995255988358 7322024001655 7431316569685 7734072328972 7842738940325 7949154532225 8052987872380 8162256264140 8273007283420 8614145884300 8742725376100 8788718555650 8861352593300 8931495640276 9052684220228 9616997913710 9667590411215 9747487852630 10066234840475 10149426863950 10202820330175 10287141159350 10341259104275 10578697705081 10666124958842 10722236637893 10810850163826 11164369550345 11256637067290 11315855275285 11373635777900 12382300774019 12445526711860 12614396044580 13312770912100 13690079383046 13803220534972 13875835649038 13990511976716 14644048003310 14862633139370 15556908389825 15685477880650 15767995055725 15898309064450 16348896453307 17254025668715 17488139970895 17577437111300 19136283014393 19233995827420 19335180822430 19494975705260 20132469680950 20298853727900 20405640660350 20574282318700 20682518208550 21157395410162 21332249917684 21444473275786 21621700327652 22328739100690 22513274134580 22631710550570 24042494784275 24368719631575 24561613010759 24764601548038 24894881605627 25266476336929 26665312397105 27027125409565 27380158766092 27751671298076 28141592668225 29288096006620 29725266278740 31113816779650 31370955761300 31535990111450 31796618128900 32697792906614 34225198457615 34508051337430 34689589122595 34976279941790 36610120008275 37156582848425 37958856471173 38272566028786 38473907935969 38670361644860 40264939361900 40811281320700 41365036417100 42314790820324 42888946551572 44657478201380 45263421101140 48084989568550 48337952056075 48737439263150 49123226021518 49529203096076 49789763211254 50532952673858 52893488525405 53330624794210 53611183189465 54054250819130 55821847751725 56283185336450 56579276376425 58663687273631 59459675901043 61911503870095 62227633559300 63071980222900 65395585813228 68450396915230 69016102674860 69379178245190 69952559883580 73220240016550 74313165696850 75917712942346 76545132057572 76947815871938 81744482266535 86270128343575 87440699854475 90662062150157 95681415071965 96169979137100 96675904112150 97474878526300 98246452043036 99579526422508 101065905347716 105786977050810 106661249588420 107222366378930 108108501638260 111643695503450 112566370672900 113158552752850 116365674755891 117327374547262 117944603016823 118919351802086 122808065053795 123823007740190 124474408028135 126332381684645 133326561985525 135135627047825 136205308514209 136900793830460 138758356490380 146440480033100 148626331393700 151835425884692 153895631743876 163488964533070 171125992288075 172540256687150 173447945612975 174881399708950 179837860986377 181324124300314 189794282355865 191362830143930 192369539679845 193351808224300 210499113158323 211573954101620 214444732757860 223287391006900 226317105505700 232731349511782 234654749094524 235889206033646 237838703604172 245616130107590 247646015480380 248948816056270 252664763369290 264467442627025 266653123971050 268055915947325 270271254095650 272410617028418 277931239706219 293318436368155 297298379505215 309557519350475 325316811244681 326977929066140 342251984576150 345080513374300 346895891225950 349762799417900 359675721972754 362648248600628 379588564711730 382725660287860 384739079359690 408722411332675 417547421182903 420998226316646 423212987295659 453310310750785 465462699023564 471778412067292 478407075359825 491232260215180 497897632112540 505329526738580 528934885254050 533306247942100 536111831894650 540542508191300 544821234056836 555862479412438 581828373779455 586636872736310 589723015084115 594596759010430 614040325268975 619115038700950 622372040140675 631661908423225 645300560009941 650633622489362 654056434911473 681026542571045 684503969152300 693791782451900 719351443945508 759177129423460 769478158719380 817444822665350 835094842365806 841996452633292 846425974591318 899189304931885 906620621501570 948971411779325 956814150719650 961847698399225 997282683651727 1052495565791615 1057869770508100 1072223663789300 1111724958824876 1163656747558910 1173273745472620 1179446030168230 1189193518020860 1228080650537950 1238230077401900 1244744080281350 1263323816846450 1290601120019882 1301267244978724 1308112869822946 1362053085142090 1389656198531095 1466592181840775 1486491897526075 1498258393656299 1541255056552669 1626584056223405 1634889645330700 1670189684731612 1692851949182636 1798378609863770 1813241243003140 1897942823558650 1913628301439300 1923695396798450 1978216470850147 1994565367303454 2087737105914515 2104991131583230 2116064936478295 2266551553753925 2315490244741553 2327313495117820 2358892060336460 2456161301075900 2489488160562700 2526647633692900 2581202240039764 2616225739645892 2724106170284180 2779312397062190 2909141868897275 2933184363681550 2948615075420575 2972983795052150 2996516787312598 3057243636768409 3082510113105338 3226502800049705 3253168112446810 3270282174557365 3405132712855225 3578484923691491 3596757219727540 3795885647117300 3847390793596900 3956432941700294 3989130734606908 4175474211829030 4209982263166460 4232129872956590 4495946524659425 4533103107507850 4630980489483106 4986413418258635 5262477828958075 5530385791159577 5558624794124380 5818283737794550 5866368727363100 5897230150841150 5945967590104300 5993033574625196 6114487273536818 6165020226210676 6453005600099410 6506336224893620 6540564349114730 6810265425710450 6948280992655475 7098306160109351 7156969847382982 7194620784026203 7491291968281495 7706275282763345 7912865883400588 8132920281117025 8350948423658060 8464259745913180 8991893049318850 9066206215015700 9261960978966212 9891082354250735 9972826836517270 10438685529572575 10524955657916150 10580324682391475 10970109520168997 11060771582319154 11577451223707765 11636567475589100 11794460301682300 12228974547073636 12906011200198820 13081128698229460 13620530851420900 13896561985310950 14196612320218702 14313939694765964 14389241568052406 14982583936562990 15286218183842045 15412550565526690 16132514000248525 16265840562234050 16351410872786825 16953805622079359 17892424618457455 17983786098637700 19782164708501470 19945653673034540 20877371059145150 21049911315832300 21160649364782950 21940219040337994 22121543164638308 23154902447415530 24932067091293175 25470392692157083 27651928955797885 27793123970621900 28393224640437404 28778483136104812 29965167873125980 30572436367684090 30825101131053380 32265028000497050 32531681124468100 32702821745573650 33629680004452499 33907611244158718 35491530800546755 35784849236914910 35973103920131015 37456459841407475 38531376413816725 39363334160606401 39564329417002940 41754742118290300 42321298729565900 43880438080675988 46309804894831060 49455411771253675 49864134182586350 50940785384314166 54850547600844985 55303857911595770 57887256118538825 60834243702755347 61144872735368180 64530056000994100 65405643491147300 67259360008904998 67815222488317436 70983061601093510 71569698473829820 71946207840262030 74912919682814950 76431090919210225 77062752827633450 78726668321212802 84769028110396795 89462123092287275 94016558449712809 98910823542507350 99728268365172700 101881570768628332 109701095201689970 110607715823191540 115774512237077650 120671204721858967 121668487405510694 127351963460785415 134518720017809996 138259644778989425 141966123202187020 143892415680524060 149825839365629900 152862181838420450 154125505655266900 157453336642425604 168148400022262495 169538056220793590 177457654002733775 178924246184574550 179865519600655075 186491861842872949 188033116899425618 196816670803032005 197821647085014700 219402190403379940 231549024474155300 241342409443717934 243336974811021388 254703926921570830 274252738004224925 276519289557978850 304171218513776735 305724363676840900 336296800044524990 339076112441587180 354915308005467550 357848492369149100 359731039201310150 372983723685745898 376066233798851236 393633341606064010 423845140551983975 432996675766670411 470082792248564045 482684818887435868 509407853843141660 548505476008449850 553038579115957700 603356023609294835 608342437027553470 636759817303927075 669176680730308817 672593600089049980 709830616010935100 719462078402620300 745967447371491796 787266683212128020 840742000111312475 847690281103967950 865993351533340822 932459309214364745 940165584497128090 984083354015160025 1034182142946840899 1097010952016899700 1206712047218589670 1216684874055106940 1273519634607854150 1338353361460617634 1520856092568883675 1681484000222624950 1695380562207935900 1731986703066681644 1864918618428729490 1880331168994256180 1968166708030320050 2051410480271602439 2068364285893681798 2164983378833352055 2350413961242820225 2413424094437179340 2547039269215708300 2676706722921235268 3016780118046474175 3041712185137767350 3345883403651544085 3362968000445249900 3729837236857458980 3936333416060640100 4102820960543204878 4136728571787363596 4329966757666704110 4662296546071823725 4700827922485640450 5170910714734204495 6033560236092948350 6083424370275534700 6691766807303088170 7360943488033396987 8205641921086409756 8659933515333408220 9324593092143647450 9401655844971280900 10257052401358012195 10341821429468408990 10824916894166760275 11376003572415249889 12067120472185896700 13383533614606176340 14721886976066793974 16729417018257720425 18649186184287294900 20514104802716024390 20683642858936817980 21649833788333520550 22752007144830499778 25854553573671022475 29443773952133587948 33458834036515440850 36804717440166984935 41028209605432048780 43299667576667041100 45504014289660999556 51285262006790060975 51709107147342044950 56880017862076249445 66917668073030881700 73609434880333969870 102570524013580121950 103418214294684089900 113760035724152498890 125136039296567748779 147218869760667939740 184023587200834924675 205141048027160243900 227520071448304997780 250272078593135497558 284400089310381247225 368047174401669849350 500544157186270995116 568800178620762494450 625680196482838743895 736094348803339698700 1137600357241524988900 1251360392965677487790 2502720785931354975580 3128400982414193719475 6256801964828387438950 12513603929656774877900
- Sum of all divisors σ(n): 32265279707789151229752
- Sum of proper divisors (its aliquot sum) s(n): 19751675778132376351852
- 12513603929656774877900 is an abundant number, because the sum of its proper divisors (19751675778132376351852) is greater than itself. Its abundance is 7238071848475601473952
Bases of 12513603929656774877900
- Binary: 101010011001011101001000111101101000011011100101000100011111100010110011002
- Hexadecimal: 0x2A65D23DA1B9447E2CC
- Base-36: 21CWHUZM4GNLNT8
Squares and roots of 12513603929656774877900
- 12513603929656774877900 squared (125136039296567748779002) is 156590283308321478426547223778440559908410000
- 12513603929656774877900 cubed (125136039296567748779003) is 1959508784553079335033679324425479052978508531529143612933139000000
-
The
square root of 12513603929656774877900 is 111864220954.0511432865 -
The
cube root of 12513603929656774877900 is 23216360.2954028561
Scales and comparisons
How big is 12513603929656774877900?- 12,513,603,929,656,774,877,900 seconds is equal to 293,274,701,009 years, 3 weeks, 3 days, 15 hours, 30 minutes, 7 seconds.
-
To count from 1 to 12,513,603,929,656,774,877,900 would take you about two hundred ninety-three billion, two hundred seventy-four million, seven hundred one thousand and nine years!
This is a very rough estimate, based on a speaking rate of half a second every third order of magnitude. If you speak quickly, you could probably say any randomly-chosen number between one and a thousand in around half a second. Very big numbers obviously take longer to say, so we add half a second for every extra x1000. (We do not count involuntary pauses, bathroom breaks or the necessity of sleep in our calculation!)
- A cube with a volume of 12513603929656774877900 cubic inches would be around 1934696.7 feet tall.
Recreational maths with 12513603929656774877900
- 12513603929656774877900 backwards is 00977847765692930631521
- The number of decimal digits it has is: 23
- The sum of 12513603929656774877900's digits is 107
- More coming soon!
Link to this page
HTML: To link to this page, just copy and paste the link below into your blog, web page or email.
BBCODE: To link to this page in a forum post or comment box, just copy and paste the link code below:
Cite this page
MLA style:
"Number 12513603929656774877900 - Facts about the integer". Numbermatics.com. 2024. Web. 10 June 2024.
APA style:
Numbermatics. (2024). Number 12513603929656774877900 - Facts about the integer. Retrieved 10 June 2024, from https://numbermatics.com/n/12513603929656774877900/
Chicago style:
Numbermatics. 2024. "Number 12513603929656774877900 - Facts about the integer". https://numbermatics.com/n/12513603929656774877900/
The information we have on file for 12513603929656774877900 includes mathematical data and numerical statistics calculated using standard algorithms and methods. We are adding more all the time. If there are any features you would like to see, please contact us. Information provided for educational use, intellectual curiosity and fun!
Keywords: Divisors of 12513603929656774877900, math, Factors of 12513603929656774877900, curriculum, school, college, exams, university, Prime factorization of 12513603929656774877900, STEM, science, technology, engineering, physics, economics, calculator, twelve sextillion, five hundred thirteen quintillion, six hundred three quadrillion, nine hundred twenty-nine trillion, six hundred fifty-six billion, seven hundred seventy-four million, eight hundred seventy-seven thousand, nine hundred.