52024524337500
52,024,524,337,500 is an even composite number composed of nine prime numbers multiplied together.
52024524337500 is an even composite number. It is composed of nine distinct prime numbers multiplied together. It has a total of two thousand, three hundred four divisors.
Prime factorization of 52024524337500:
22 × 3 × 55 × 11 × 13 × 17 × 31 × 41 × 449
(2 × 2 × 3 × 5 × 5 × 5 × 5 × 5 × 11 × 13 × 17 × 31 × 41 × 449)See below for interesting mathematical facts about the number 52024524337500 from the Numbermatics database.
Names of 52024524337500
- Cardinal: 52024524337500 can be written as Fifty-two trillion, twenty-four billion, five hundred twenty-four million, three hundred thirty-seven thousand, five hundred.
Scientific notation
- Scientific notation: 5.20245243375 × 1013
Factors of 52024524337500
Divisors of 52024524337500
- Number of divisors d(n): 2304
-
Complete list of divisors:
1 2 3 4 5 6 10 11 12 13 15 17 20 22 25 26 30 31 33 34 39 41 44 50 51 52 55 60 62 65 66 68 75 78 82 85 93 100 102 110 123 124 125 130 132 143 150 155 156 164 165 170 186 187 195 204 205 220 221 246 250 255 260 275 286 300 310 325 330 340 341 372 374 375 390 403 410 425 429 442 449 451 465 492 500 510 527 533 550 561 572 615 620 625 650 660 663 682 697 715 748 750 775 780 806 820 825 850 858 884 898 902 930 935 975 1020 1023 1025 1054 1066 1100 1105 1122 1209 1230 1250 1271 1275 1300 1326 1347 1353 1364 1375 1394 1430 1500 1550 1581 1599 1612 1625 1650 1700 1705 1716 1796 1804 1860 1870 1875 1950 2015 2046 2050 2091 2108 2125 2132 2145 2210 2244 2245 2255 2325 2418 2431 2460 2500 2542 2550 2635 2652 2665 2694 2706 2750 2788 2805 2860 3075 3100 3125 3162 3198 3250 3300 3315 3410 3485 3575 3740 3750 3813 3875 3900 4030 4092 4100 4125 4182 4250 4290 4420 4433 4490 4510 4650 4675 4836 4862 4875 4939 5084 5100 5115 5125 5270 5330 5388 5412 5500 5525 5610 5797 5837 5863 6045 6150 6250 6324 6355 6375 6396 6500 6630 6735 6765 6820 6851 6875 6970 7150 7293 7500 7626 7633 7667 7750 7905 7995 8060 8125 8250 8364 8500 8525 8580 8866 8980 9020 9061 9300 9350 9375 9724 9750 9878 10075 10230 10250 10455 10540 10625 10660 10725 11050 11220 11225 11275 11594 11625 11674 11726 12090 12155 12300 12500 12710 12750 13175 13260 13299 13325 13470 13530 13702 13750 13919 13940 13981 14025 14300 14586 14817 15252 15266 15334 15375 15500 15810 15990 16250 16500 16523 16575 17050 17391 17425 17511 17589 17732 17875 18122 18409 18700 18750 19065 19375 19500 19756 20150 20460 20500 20553 20625 20910 21250 21450 21607 22100 22165 22450 22550 22899 23001 23188 23250 23348 23375 23452 24180 24310 24375 24695 25420 25500 25575 25625 26350 26598 26650 26940 27060 27183 27404 27500 27625 27838 27962 28050 28985 29172 29185 29315 29634 30225 30532 30668 30750 31620 31775 31875 31980 32500 33046 33150 33675 33825 34100 34255 34375 34782 34850 35022 35178 35750 36244 36465 36818 37500 38130 38165 38335 38750 39525 39975 40300 40625 41106 41250 41757 41820 41943 42500 42625 42900 43214 44330 44900 45100 45305 45798 46002 46500 46750 48620 48750 49390 49569 50375 51150 51250 52275 52700 53125 53196 53300 53625 54366 55227 55250 55676 55924 56100 56125 56375 57970 58125 58370 58630 59268 60450 60775 61500 63550 63750 64207 64821 65875 66092 66300 66495 66625 67350 67650 68510 68750 69564 69595 69700 69905 70044 70125 70356 71500 72930 73636 74085 75361 76260 76330 76670 76875 77500 79050 79950 81250 82212 82500 82615 82875 83514 83886 83963 85250 86428 86955 87125 87555 87945 88660 89375 90610 91596 92004 92045 93500 95325 96875 97500 98780 99138 99229 99671 100750 102300 102500 102765 103125 104550 106250 107250 108035 108732 110454 110500 110825 112250 112750 114495 115005 115940 116250 116740 116875 117260 120900 121550 121875 123475 127100 127500 127875 128125 128414 129642 131750 132990 133250 134700 135300 135915 137020 137500 138125 139190 139810 140250 144925 145860 145925 146575 148170 150722 151125 152660 153109 153340 153750 158100 158875 159375 159900 162500 165230 165750 167028 167772 167926 168375 169125 170500 171275 173910 174250 175110 175890 178750 180947 181220 181753 182325 184090 190650 190825 191675 192621 193750 197625 198276 198458 199342 199875 201500 202499 205530 206250 208785 209100 209715 212500 213125 214500 216070 220908 221650 224500 225500 226083 226525 228990 230010 232500 233750 236623 237677 239317 243100 243750 246950 247845 251875 251889 255750 256250 256828 259284 261375 263500 265980 266500 268125 271830 276135 276250 278380 279620 280500 280625 280891 281875 289850 290625 291850 293150 296340 297687 299013 301444 302250 303875 306218 307500 312953 317750 318750 321035 324105 329375 330460 331500 332475 333125 335852 336750 338250 342550 347820 347975 348500 349525 350220 350625 351780 357500 361894 363506 364650 368180 370425 376805 381300 381650 383350 384375 385242 387500 395250 396916 398684 399750 404998 411060 412500 413075 414375 417570 419430 419815 426250 432140 434775 435625 437775 439725 443300 446875 452166 453050 457980 459327 460020 460225 467500 473246 475354 476625 478634 487500 493900 495690 496145 498355 503750 503778 511500 512500 513825 522750 536250 540175 542841 543660 545259 552270 552500 554125 561250 561782 563750 570679 572475 575025 579700 581250 583700 584375 586300 595374 598026 604500 607497 607750 612436 617375 625906 635500 637500 639375 642070 648210 658750 664950 666250 673500 676500 679575 685100 690625 695950 699050 701250 709869 713031 717951 723788 724625 727012 729300 729625 732875 740850 753610 755625 763300 765545 766700 768750 770484 790500 794375 799500 809996 826150 828750 835140 838860 839630 841875 842673 845625 852500 856375 869550 871250 875550 879450 893750 904332 904735 906100 908765 911625 918654 920450 938859 946492 950708 953250 954125 957268 958375 963105 988125 991380 992290 996710 999375 1007500 1007556 1012495 1027650 1043925 1045500 1048575 1065625 1072500 1080350 1085682 1090518 1091519 1104540 1108250 1122500 1123564 1127500 1130415 1132625 1141358 1144950 1150050 1162500 1168750 1183115 1188385 1190748 1196052 1196585 1214994 1215500 1234750 1239225 1251812 1259375 1259445 1278750 1284140 1296420 1306875 1317500 1329900 1332500 1340625 1359150 1380675 1381250 1391900 1398100 1402500 1403125 1404455 1409375 1419738 1426062 1435902 1449250 1459250 1465750 1481700 1488435 1495065 1507220 1511250 1519375 1531090 1537500 1564765 1588750 1605175 1620525 1646875 1652300 1657500 1662375 1665625 1679260 1683750 1685346 1691250 1712037 1712750 1739100 1739875 1742500 1747625 1751100 1753125 1758900 1787500 1809470 1817530 1823250 1837308 1840900 1852125 1877718 1884025 1906500 1908250 1916750 1926210 1976250 1984580 1990417 1993420 1998750 2024990 2055300 2065375 2071875 2087850 2097150 2099075 2131250 2160700 2171364 2173875 2178125 2181036 2183038 2188875 2198625 2216500 2260830 2265250 2282716 2289900 2296635 2300100 2301125 2337500 2366230 2376770 2383125 2393170 2429988 2469500 2478450 2480725 2491775 2518750 2518890 2557500 2569125 2602853 2613750 2632487 2681250 2700875 2714205 2718300 2726295 2761350 2762500 2770625 2806250 2808910 2818750 2839476 2852124 2853395 2862375 2871804 2875125 2898500 2918500 2931500 2976870 2990130 3022500 3037485 3038750 3062180 3076099 3086875 3089801 3129530 3177500 3196875 3210350 3241050 3274557 3293750 3324750 3331250 3367500 3370692 3382500 3397875 3424074 3425500 3442483 3479750 3495250 3506250 3549345 3565155 3589755 3618940 3623125 3635060 3646500 3648125 3664375 3704250 3755436 3768050 3778125 3816500 3827725 3833500 3852420 3952500 3971875 3980834 3997500 4049980 4068389 4130750 4143750 4175700 4194300 4198150 4209375 4213365 4228125 4262500 4281875 4347750 4356250 4366076 4377750 4397250 4521660 4523675 4530500 4543825 4558125 4593270 4602250 4694295 4732460 4753540 4766250 4770625 4786340 4791875 4815525 4940625 4956900 4961450 4983550 4996875 5037500 5037780 5062475 5138250 5205706 5219625 5227500 5242875 5264974 5362500 5401750 5428410 5452590 5457595 5522700 5541250 5612500 5617820 5637500 5652075 5663125 5706790 5724750 5750250 5915575 5941925 5953740 5971251 5980260 5982925 6074970 6077500 6152198 6173750 6179602 6196125 6259060 6277469 6297225 6393750 6420700 6482100 6534375 6549114 6587500 6649500 6662500 6795750 6848148 6884966 6903375 6959500 6990500 7012500 7022275 7098690 7130310 7179510 7246250 7296250 7328750 7408500 7418827 7442175 7475325 7536100 7556250 7596875 7655450 7808559 7823825 7897461 7943750 7961668 8025875 8102625 8136778 8261500 8287500 8311875 8396300 8418750 8426730 8456250 8560185 8563750 8695500 8699375 8712500 8738125 8755500 8794500 9047350 9087650 9116250 9186540 9204500 9228297 9260625 9269403 9388590 9420125 9532500 9541250 9583750 9631050 9701543 9881250 9922900 9952085 9967100 9993750 10124950 10276500 10326875 10327449 10411412 10439250 10485750 10495375 10529948 10803500 10856820 10869375 10905180 10915190 10944375 10993125 11082500 11304150 11326250 11413580 11449500 11483175 11500500 11505625 11831150 11883850 11915625 11942502 11965850 12149940 12205167 12304396 12347500 12359204 12392250 12403625 12458875 12554938 12594450 12787500 12845625 13014265 13068750 13098228 13162435 13504375 13571025 13591500 13631475 13769932 13806750 13853125 14044550 14197380 14260620 14266975 14311875 14359020 14375625 14492500 14592500 14657500 14837654 14884350 14950650 15112500 15187425 15193750 15310900 15380495 15434375 15449005 15617118 15647650 15794922 15887500 16051750 16205250 16273556 16372785 16623750 16837500 16853460 16912500 16989375 17120370 17127500 17212415 17398750 17476250 17746725 17825775 17948775 18094700 18115625 18175300 18232500 18240625 18321875 18456594 18521250 18538806 18777180 18832407 18840250 19082500 19138625 19167500 19262100 19403086 19762500 19904170 19987500 20249900 20341945 20653750 20654898 20878500 20971500 20990750 21066825 21409375 21738750 21830380 21888750 21986250 22256481 22608300 22618375 22652500 22719125 22790625 22966350 23011250 23471475 23662300 23767700 23831250 23853125 23885004 23931700 23959375 24077625 24410334 24784500 24807250 24917750 25109876 25188900 25312375 25691250 26028530 26098125 26137500 26214375 26324870 27008750 27142050 27262950 27287975 27613500 27706250 28089100 28260375 28315625 28533950 28623750 28751250 29104629 29577875 29675308 29709625 29768700 29856255 29901300 29914625 30374850 30387500 30760990 30868750 30898010 30980625 31234236 31295300 31387345 31486125 31589844 32103500 32410500 32745570 33247500 33837089 33978750 34240740 34424830 34516875 34797500 34952500 35111375 35493450 35651550 35897550 36231250 36481250 36643750 36913188 37042500 37077612 37094135 37210875 37376625 37664814 37680500 38277250 38806172 39042795 39119125 39487305 39808340 40129375 40513125 40683890 41307500 41309796 41559375 41981500 42133650 42800925 42818750 43477500 43496875 43690625 43777500 43972500 44512962 44752279 45236750 45438250 45581250 45932700 46022500 46141485 46303125 46347015 46942950 47100625 47662500 47706250 47918750 48155250 48507715 48820668 49614500 49760425 49835500 50624750 51382500 51634375 51637245 52057060 52196250 52428750 52476875 52649740 54017500 54284100 54346875 54525900 54575950 54721875 54965625 55412500 56520750 56631250 57067900 57247500 57415875 57502500 57528125 58209258 59155750 59419250 59712510 59829250 60749700 61025835 61521980 61737500 61796020 61961250 62018125 62294375 62774690 62972250 64228125 65071325 65491140 65812175 67521875 67674178 67855125 67957500 68157375 68849660 69033750 70222750 70986900 71303100 71334875 71559375 71795100 71878125 72462500 72962500 73287500 74188270 74421750 74753250 75329628 75937125 76554500 76902475 77245025 78085590 78238250 78974610 80258750 81026250 81367780 81607097 81863925 83118750 84267300 84946875 85601850 85637500 86062075 86993750 87381250 88733625 89025924 89128875 89504558 89743875 90473500 90876500 91162500 92282970 92606250 92694030 93885900 94162035 94201250 95412500 95693125 95837500 96310500 97015430 99520850 101249500 101511267 101709725 103268750 103274490 104392500 104857500 104953750 105334125 106716973 108693750 109151900 109443750 109931250 111282405 113041500 113091875 113262500 113595625 114831750 115056250 116418516 117357375 118311500 118838500 119425020 119658500 120388125 122051670 123922500 124036250 124588750 125549380 125944500 126120059 126561875 128456250 130142650 130490625 131071875 131624350 134256837 135043750 135348356 135710250 136314750 136439875 138067500 140445500 141301875 142669750 143118750 143756250 145523145 147889375 148376540 148548125 148843500 149281275 149506500 149573125 151874250 153804950 154490050 154903125 156171180 156476500 156936725 157430625 157949220 160517500 162052500 163214194 163727850 166237500 169185445 169893750 171203700 172124150 172584375 173987500 174762500 175556875 177467250 178257750 179009116 179487750 184565940 185212500 185388060 185470675 186054375 186883125 188324070 188402500 191386250 194030860 195213975 195595625 197436525 199041700 200646875 202565625 203022534 203419450 206537500 206548980 209907500 210668250 213433946 214004625 217387500 218887500 219862500 222564810 223761395 226183750 227191250 229663500 230112500 230707425 231735075 234714750 235503125 240776250 242538575 244103340 244821291 248072500 248802125 249177500 252240118 253123750 256912500 258186225 260285300 260981250 262143750 262384375 263248700 268513674 270087500 271420500 272629500 272879750 282603750 285339500 286237500 287079375 287512500 291046290 295778750 297096250 298562550 299146250 303748500 305129175 307609900 308980100 309806250 310090625 311471875 313873450 314861250 320150919 325356625 326428388 327455700 329060875 338370890 339275625 339787500 340786875 344248300 345168750 351113750 354934500 356515500 356674375 358975500 370941350 372108750 373766250 376648140 378360177 379685625 382772500 384512375 386225125 390427950 391191250 394873050 401293750 405131250 406045068 406838900 408035485 409319625 421336500 426867892 428009250 430310375 443668125 445129620 445644375 447522790 448719375 452367500 454382500 461414850 463470150 469429500 470810175 471006250 478465625 481552500 485077150 489642582 497604250 504480236 506247500 507556335 508548625 516372450 521962500 524287500 524768750 526670625 533584865 537027348 545759500 556412025 565207500 565459375 567978125 574158750 582092580 586786875 591557500 594192500 597125100 598292500 601940625 610258350 619612500 620181250 622943750 627746900 629722500 630600295 632809375 640301838 650713250 658121750 671284185 676741780 678551250 681573750 682199375 690337500 702227500 706509375 713348750 727615725 739446875 741882700 742740625 744217500 746406375 747532500 747865625 756720354 759371250 769024750 772450250 780855900 782382500 784683625 787153125 789746100 802587500 810262500 816070970 818639250 845927225 856018500 860620750 877784375 887336250 891288750 895045580 897438750 922829700 926940300 927353375 930271875 934415625 941620350 942012500 956931250 970154300 976069875 977978125 979285164 987182625 995208500 1015112670 1017097250 1032744900 1049537500 1053341250 1067169730 1070023125 1112824050 1118806975 1130918750 1135956250 1148317500 1153537125 1158675375 1173573750 1203881250 1212692875 1220516700 1224106455 1240362500 1244010625 1245887500 1261200590 1265618750 1280603676 1290931125 1301426500 1316243500 1342568370 1357102500 1363147500 1364398750 1387320649 1413018750 1426697500 1435396875 1455231450 1478893750 1485481250 1492812750 1495731250 1513440708 1518742500 1525645875 1538049500 1544900500 1569367250 1574306250 1600754595 1626783125 1632141940 1637278500 1645304375 1691854450 1696378125 1703934375 1721241500 1755568750 1774672500 1782577500 1783371875 1794877500 1854706750 1860543750 1868831250 1883240700 1891800885 1898428125 1913862500 1922561875 1931125625 1952139750 1955956250 1974365250 2030225340 2034194500 2040177425 2046598125 2106682500 2134339460 2140046250 2151551875 2218340625 2225648100 2228221875 2237613950 2243596875 2261837500 2271912500 2307074250 2317350750 2347147500 2354050875 2407762500 2425385750 2448212910 2488021250 2522401180 2531237500 2537781675 2542743125 2581862250 2633353125 2667924325 2685136740 2728797500 2774641298 2782060125 2826037500 2870793750 2910462900 2933934375 2957787500 2970962500 2985625500 2991462500 3051291750 3138734500 3148612500 3153001475 3201509190 3253566250 3290608750 3356420925 3383708900 3392756250 3407868750 3410996875 3511137500 3566743750 3638078625 3709413500 3721087500 3732031875 3737662500 3783601770 3796856250 3845123750 3862251250 3904279500 3911912500 3923418125 3948730500 4080354850 4093196250 4161961947 4229636125 4280092500 4303103750 4436681250 4456443750 4475227900 4487193750 4614148500 4634701500 4636766875 4708101750 4850771500 4880349375 4896425820 4935913125 4976042500 5075563350 5085486250 5163724500 5266706250 5335848650 5350115625 5549282596 5564120250 5594034875 5741587500 5767685625 5793376875 5867868750 6063464375 6102583500 6120532275 6220053125 6306002950 6403018380 6454655625 6507132500 6581217500 6712841850 6785512500 6815737500 6821993750 6936603245 7133487500 7276157250 7464063750 7567203540 7593712500 7628229375 7690247500 7724502500 7846836250 8003772975 8133915625 8160709700 8186392500 8226521875 8323923894 8459272250 8606207500 8873362500 8912887500 8974387500 9273533750 9416203500 9459004425 9612809375 9655628125 9760698750 9871826250 10151126700 10170972500 10200887125 10232990625 10533412500 10671697300 10700231250 10757759375 11128240500 11188069750 11535371250 11586753750 11735737500 11770254375 12126928750 12241064550 12440106250 12612005900 12688908375 12713715625 12909311250 13339621625 13425683700 13643987500 13873206490 13910300625 14552314500 14928127500 15256458750 15693672500 15765007375 16007545950 16267831250 16453043750 16647847788 16782104625 16918544500 18190393125 18547067500 18660159375 18918008850 19225618750 19311256250 19521397500 19617090625 19743652500 20401774250 20465981250 20809809735 21148180625 21400462500 21515518750 22376139500 23070742500 23173507500 23183834375 23540508750 24253857500 24401746875 24482129100 24679565625 24880212500 25377816750 25427431250 25818622500 26679243250 27746412980 27820601250 27970174375 28838428125 28966884375 30317321875 30512917500 30602661375 31530014750 32015091900 32273278125 32535662500 32906087500 33564209250 34683016225 36380786250 37320318750 37836017700 38141146875 38451237500 38622512500 39234181250 40018864875 40803548500 40931962500 41619619470 42296361250 43031037500 46367668750 47081017500 47295022125 48803493750 49359131250 50755633500 50854862500 51004435625 53358486500 55641202500 55940348750 57676856250 57933768750 58851271875 60634643750 61205322750 63060029500 63444541875 64546556250 66698108125 67128418500 69366032450 69551503125 72761572500 74640637500 76282293750 78468362500 78825036875 80037729750 83239238940 83910523125 84592722500 90951965625 92735337500 94590044250 97606987500 98718262500 102008871250 104049048675 105740903125 111880697500 115353712500 115867537500 117702543750 121269287500 122410645500 126889083750 129093112500 133396216250 138732064900 139103006250 139850871875 152564587500 153013306875 157650073750 160075459500 167821046250 173415081125 181903931250 189180088500 200094324375 204017742500 208098097350 211481806250 235405087500 236475110625 253778167500 255022178125 266792432500 278206012500 279701743750 306026613750 315300147500 317222709375 333490540625 335642092500 346830162250 363807862500 394125184375 400188648750 416196194700 419552615625 422963612500 472950221250 510044356250 520245243375 559403487500 612053227500 634445418750 666981081250 693660324500 765066534375 788250368750 800377297500 839105231250 867075405625 945900442500 1000471621875 1020088712500 1040490486750 1182375553125 1268890837500 1333962162500 1530133068750 1576500737500 1678210462500 1734150811250 2000943243750 2080980973500 2364751106250 2601226216875 3060266137500 3468301622500 4001886487500 4335377028125 4729502212500 5202452433750 8670754056250 10404904867500 13006131084375 17341508112500 26012262168750 52024524337500
- Sum of all divisors σ(n): 200024797593600
- Sum of proper divisors (its aliquot sum) s(n): 148000273256100
- 52024524337500 is an abundant number, because the sum of its proper divisors (148000273256100) is greater than itself. Its abundance is 95975748918600
Bases of 52024524337500
- Binary: 10111101010000111001110100101011110001010111002
- Hexadecimal: 0x2F50E74AF15C
- Base-36: IFVQIK21O
Squares and roots of 52024524337500
- 52024524337500 squared (520245243375002) is 2706551132543129813906250000
- 52024524337500 cubed (520245243375003) is 140807035265678245271987549068359375000000
-
The
square root of 52024524337500 is 7212802.8073350237 -
The
cube root of 52024524337500 is 37330.9784256571
Scales and comparisons
How big is 52024524337500?- 52,024,524,337,500 seconds is equal to 1,654,218 years, 49 weeks, 3 days, 8 hours, 25 minutes.
-
To count from 1 to 52,024,524,337,500 would take you about four million, one hundred thirty-five thousand, five hundred forty-seven 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 52024524337500 cubic inches would be around 3110.9 feet tall.
Recreational maths with 52024524337500
- 52024524337500 backwards is 00573342542025
- The number of decimal digits it has is: 14
- The sum of 52024524337500's digits is 42
- 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 52024524337500 - Facts about the integer". Numbermatics.com. 2024. Web. 9 June 2024.
APA style:
Numbermatics. (2024). Number 52024524337500 - Facts about the integer. Retrieved 9 June 2024, from https://numbermatics.com/n/52024524337500/
Chicago style:
Numbermatics. 2024. "Number 52024524337500 - Facts about the integer". https://numbermatics.com/n/52024524337500/
The information we have on file for 52024524337500 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 52024524337500, math, Factors of 52024524337500, curriculum, school, college, exams, university, Prime factorization of 52024524337500, STEM, science, technology, engineering, physics, economics, calculator, fifty-two trillion, twenty-four billion, five hundred twenty-four million, three hundred thirty-seven thousand, five hundred.