27736375285468400768
27,736,375,285,468,400,768 is an even composite number composed of five prime numbers multiplied together.
27736375285468400768 is an even composite number. It is composed of five distinct prime numbers multiplied together. It has a total of one thousand, seven hundred ninety-two divisors.
Prime factorization of 27736375285468400768:
27 × 76 × 293 × 713 × 211
(2 × 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 7 × 7 × 7 × 7 × 29 × 29 × 29 × 71 × 71 × 71 × 211)See below for interesting mathematical facts about the number 27736375285468400768 from the Numbermatics database.
Names of 27736375285468400768
- Cardinal: 27736375285468400768 can be written as Twenty-seven quintillion, seven hundred thirty-six quadrillion, three hundred seventy-five trillion, two hundred eighty-five billion, four hundred sixty-eight million, four hundred thousand, seven hundred sixty-eight.
Scientific notation
- Scientific notation: 2.7736375285468400768 × 1019
Factors of 27736375285468400768
Divisors of 27736375285468400768
- Number of divisors d(n): 1792
-
Complete list of divisors:
1 2 4 7 8 14 16 28 29 32 49 56 58 64 71 98 112 116 128 142 196 203 211 224 232 284 343 392 406 422 448 464 497 568 686 784 812 841 844 896 928 994 1136 1372 1421 1477 1568 1624 1682 1688 1856 1988 2059 2272 2401 2744 2842 2954 3136 3248 3364 3376 3479 3712 3976 4118 4544 4802 5041 5488 5684 5887 5908 6119 6272 6496 6728 6752 6958 7952 8236 9088 9604 9947 10082 10339 10976 11368 11774 11816 12238 12992 13456 13504 13916 14413 14981 15904 16472 16807 19208 19894 20164 20678 21952 22736 23548 23632 24353 24389 24476 25984 26912 27008 27832 28826 29962 31808 32944 33614 35287 38416 39788 40328 41209 41356 42833 43904 45472 47096 47264 48706 48778 48952 53824 55664 57652 59711 59924 63616 65888 67228 69629 70574 72373 76832 79576 80656 82418 82712 85666 90944 94192 94528 97412 97556 97904 100891 104867 107648 111328 115304 117649 119422 119848 131776 134456 139258 141148 144746 146189 153664 159152 161312 164836 165424 170471 170723 171332 177451 181888 188384 189056 194824 195112 195808 201782 209734 222656 230608 235298 238844 239696 247009 263552 268912 278516 282296 288463 289492 292378 299831 307328 318304 322624 329672 330848 340942 341446 342664 354902 357911 376768 389648 390224 391616 403564 417977 419468 434449 445312 461216 470596 477688 479392 487403 494018 506611 537824 557032 564592 576926 578984 584756 599662 636608 645248 659344 661696 681884 682892 685328 706237 709804 715822 734069 753536 779296 780448 783232 807128 835954 838936 868898 922432 941192 955376 958784 974806 988036 1013222 1023323 1063651 1075648 1114064 1129184 1153852 1157968 1169512 1193297 1195061 1199324 1242157 1273216 1318688 1323392 1363768 1365784 1370656 1412474 1419608 1431644 1468138 1558592 1560896 1614256 1671908 1677872 1729063 1731619 1737796 1844864 1882384 1910752 1917568 1949612 1976072 2019241 2026444 2046646 2098817 2127302 2151296 2228128 2258368 2307704 2315936 2339024 2386594 2390122 2398648 2484314 2505377 2637376 2727536 2731568 2741312 2824948 2839216 2863288 2925839 2936276 3041143 3117184 3121792 3228512 3343816 3355744 3411821 3458126 3463238 3475592 3546277 3764768 3821504 3899224 3952144 4038482 4052888 4093292 4197634 4239481 4254604 4456256 4516736 4615408 4631872 4678048 4773188 4780244 4797296 4943659 4968628 5010754 5138483 5146079 5274752 5455072 5463136 5482624 5649896 5678432 5726576 5851678 5872552 6082286 6457024 6687632 6711488 6823642 6916252 6926476 6951184 7092554 7163261 7445557 7529536 7643008 7798448 7904288 8076964 8105776 8186584 8353079 8365427 8395268 8478962 8509208 8695099 8912512 9230816 9263744 9356096 9546376 9560488 9594592 9887318 9937256 10021508 10276966 10292158 10379419 10910144 10926272 11299792 11356864 11453152 11703356 11745104 12103441 12121333 12164572 12599021 12914048 13375264 13422976 13647284 13832504 13852952 13902368 14134687 14185108 14326522 14691719 14891114 15059072 15596896 15808576 16153928 16211552 16373168 16706158 16730854 16790536 16957924 17018416 17390198 17537639 18461632 18712192 19092752 19120976 19189184 19774636 19874512 20043016 20480873 20553932 20584316 20758838 21288001 21820288 21852544 22599584 22713728 22906304 23406712 23490208 24206882 24242666 24329144 24823939 25198042 26750528 27294568 27665008 27705904 27804736 28269374 28370216 28653044 29383438 29676367 29782228 30845879 31193792 31617152 32307856 32423104 32746336 33412316 33461708 33581072 33915848 34036832 34605613 34780396 35075278 35969381 36022553 36923264 38185504 38241952 38378368 39549272 39749024 40086032 40961746 41107864 41168632 41517676 42576002 45199168 45812608 46813424 46980416 48413764 48485332 48658288 49647878 50142827 50396084 52118899 53501056 54589136 55330016 55411808 55609472 56538748 56740432 57306088 58557989 58766876 59352734 59564456 60865693 61691758 62387584 64615712 64846208 65492672 66824632 66923416 67162144 67831696 68073664 69211226 69560792 70150556 71938762 72045106 72655933 75519221 76371008 76483904 79098544 79498048 80172064 81923492 82215728 82337264 83035352 84724087 84849331 85152004 88193147 90398336 93626848 93960832 96827528 96970664 97316576 98942809 99295756 100285654 100792168 102842033 104237798 109178272 110660032 110823616 113077496 113480864 114612176 117115978 117533752 118705468 119128912 121731386 122763473 122944949 123383516 129231424 130985344 133649264 133846832 134324288 135663392 136147328 138422452 139121584 140301112 143366111 143877524 144090212 145311866 149016007 151038442 152742016 152967808 158197088 158996096 160344128 163846984 164431456 164674528 166070704 169448174 169698662 170304008 176386294 187253696 193655056 193941328 194633152 197885618 198591512 200571308 201584336 205684066 207734569 208475596 215921153 218356544 221320064 221647232 226154992 226961728 229224352 234231956 235067504 237410936 238257824 242239291 243462772 245526946 245889898 246767032 251785667 252157871 258462848 267298528 267693664 268648576 271326784 276844904 278243168 280602224 286732222 287755048 288180424 290623732 298032014 301003151 302076884 316394176 320688256 327693968 328862912 329349056 332141408 338896348 339397324 340608016 350999789 352772588 364832293 365371609 374507392 387310112 387882656 389266304 395771236 397183024 401142616 403168672 409905923 411368132 415469138 416951192 426059851 431842306 436713088 452309984 453923456 458448704 468463912 470135008 474821872 476515648 484478582 486925544 491053892 491779796 493534064 503571334 504315742 508591531 528634547 534597056 535387328 542653568 553689808 556486336 561204448 573464444 575510096 576360848 581247464 593068609 593945317 596064028 602006302 604153768 617352029 632788352 655387936 657725824 658698112 664282816 677792696 678794648 681216032 701999578 705545176 719894231 729664586 730743218 774620224 775765312 791542472 794366048 802285232 806337344 819811846 822736264 830938276 833902384 852119702 859344311 860614643 863684612 894530491 904619968 916897408 936927824 940270016 949643744 953031296 968957164 973851088 982107784 983559592 987068128 1003562777 1007142668 1008631484 1017183062 1043112049 1057269094 1069194112 1070774656 1107379616 1112972672 1122408896 1146928888 1151020192 1152721696 1162494928 1186137218 1187890634 1192128056 1204012604 1208307536 1234704058 1310775872 1328565632 1355585392 1357589296 1362432064 1403999156 1411090352 1439788462 1454141983 1459329172 1461486436 1511448071 1549240448 1551530624 1583084944 1588732096 1604570464 1612674688 1639623692 1645472528 1661876552 1667804768 1704239404 1718688622 1721229286 1727369224 1762499669 1765105097 1789060982 1809239936 1873855648 1880540032 1899287488 1937914328 1947702176 1964215568 1967119184 1974136256 2007125554 2014285336 2017262968 2034366124 2086224098 2107022057 2114538188 2190057409 2214759232 2244817792 2293857776 2302040384 2305443392 2324989856 2372274436 2375781268 2384256112 2408025208 2416615072 2456998523 2469408116 2553826051 2557601263 2621551744 2711170784 2715178592 2724864128 2807998312 2822180704 2869341461 2879576924 2908283966 2918658344 2922972872 2982418957 3022896142 3166169888 3177464192 3209140928 3279247384 3290945056 3323753104 3335609536 3408478808 3437377244 3442458572 3454738448 3524999338 3530210194 3560140717 3578121964 3700441829 3747711296 3798574976 3875828656 3895404352 3928431136 3934238368 3948272512 4014251108 4028570672 4034525936 4068732248 4157617219 4172448196 4214044114 4229076376 4321464203 4380114818 4429518464 4587715552 4604080768 4610886784 4649979712 4744548872 4751562536 4768512224 4816050416 4833230144 4913997046 4938816232 5107652102 5115202526 5422341568 5430357184 5615996624 5644361408 5738682922 5759153848 5816567932 5837316688 5845945744 5964837914 6015410177 6024302501 6045792284 6261713437 6332339776 6418281856 6558494768 6581890112 6647506208 6671219072 6816957616 6874754488 6884917144 6909476896 7024939439 7049998676 7060420388 7120281434 7156243928 7301784343 7400883658 7495422592 7751657312 7790808704 7856862272 7868476736 8028502216 8057141344 8069051872 8137464496 8315234438 8344896392 8428088228 8458152752 8642928406 8729091379 8760229636 9175431104 9299959424 9489097744 9503125072 9537024448 9632100832 9666460288 9827994092 9877632464 10178993881 10215304204 10230405052 10580136497 10844683136 10860714368 11231993248 11288722816 11477365844 11518307696 11633135864 11674633376 11691891488 11929675828 12030820354 12048605002 12091584568 12355735679 12523426874 12664679552 13116989536 13163780224 13295012416 13633915232 13749508976 13769834288 13818953792 14049878878 14099997352 14120840776 14240562868 14312487856 14603568686 14749154399 14801767316 15330401863 15503314624 15713724544 15736953472 16057004432 16114282688 16138103744 16274928992 16630468876 16689792784 16856176456 16916305504 17198989661 17285856812 17458182758 17520459272 17876782357 17903208841 18350862208 18978195488 19006250144 19074048896 19264201664 19655988184 19755264928 20357987762 20430608408 20460810104 20876932699 21160272994 22463986496 22954731688 23036615392 23266271728 23349266752 23383782976 23859351656 24061640708 24097210004 24183169136 24711471358 24920985019 25046853748 25903092803 25941384239 26233979072 26590024832 27267830464 27499017952 27539668576 27637907584 28099757756 28199994704 28241681552 28481125736 28624975712 29103320533 29207137372 29498308798 29603534632 30250249421 30660803726 31006629248 32114008864 32228565376 32276207488 32549857984 33260937752 33379585568 33712352912 33832611008 34397979322 34571713624 34916365516 35040918544 35753564714 35806417682 37956390976 38012500288 38528403328 39311976368 39510529856 40715975524 40861216816 40921620208 41753865398 42107871239 42170117507 42320545988 43831994059 44927972992 45909463376 46073230784 46532543456 46698533504 46767565952 47718703312 48123281416 48194420008 48366338272 49422942716 49841970038 50093707496 51112490401 51806185606 51882768478 52467958144 54535660928 54998035904 55079337152 56199515512 56399989408 56483363104 56962251472 57249951424 58206641066 58414274744 58996617596 59207069264 60500498842 61103639653 61321607452 63511664861 64228017728 65099715968 66521875504 66759171136 67424705824 67665222016 68795958644 69143427248 69832731032 70081837088 71252957167 71507129428 71612835364 74060955479 75912781952 76025000576 78623952736 79021059712 81431951048 81722433632 81843240416 83507730796 84215742478 84340235014 84641091976 86490149753 87663988118 91818926752 92146461568 93065086912 95437406624 96246562832 96388840016 96732676544 98845885432 99683940076 100187414992 102224980802 103244080793 103612371212 103765536956 107312813041 109996071808 110158674304 112399031024 112799978816 112966726208 113924502944 114499902848 116413282132 116828549488 117993235192 118414138528 121000997684 122207279306 122643214904 125137476499 125322461887 127023329722 128456035456 133043751008 133518342272 134849411648 137591917288 138286854496 139665462064 140163674176 142505914334 143014258856 143225670728 148121910958 157247905472 162863902096 163444867264 163686480832 167015461592 168431484956 168680470028 169282183952 172980299506 174446895133 175327976236 181321649621 181589689673 183637853504 186130173824 190874813248 192493125664 192777680032 193465353088 197691770864 199367880152 200374829984 203723243731 204449961604 206488161586 207224742424 207531073912 211751745947 214625626082 224798062048 225599957632 225933452416 227849005888 232826564264 233657098976 235986470384 236828277056 242001995368 244414558612 245286429808 250274952998 250644923774 254046659444 266087502016 269698823296 275183834576 276573708992 279330924128 280327348352 285011828668 286028517712 286451341456 295190822549 296243821916 306823958413 314495810944 325727804192 326889734528 327372961664 334030923184 336862969912 337360940056 338564367904 345960599012 348893790266 350655952472 362643299242 363179379346 367275707008 381749626496 384986251328 385555360064 395383541728 398735760304 400749659968 407446487462 408899923208 412976323172 414449484848 415062147824 423503491894 427725477571 429251252164 444581654027 449596124096 455698011776 465653128528 467314197952 471972940768 473656554112 484003990736 488829117224 490572859616 498770700169 500549905996 501289847548 508093318888 518426688353 532175004032 550367669152 553147417984 558661848256 570023657336 572057035424 572902682912 590381645098 592487643832 605431048271 613647916826 651455608384 668061846368 673725939824 674721880112 677128735808 691921198024 697787580532 701311904944 722708565551 725286598484 726358758692 751189691287 769972502656 771110720128 790767083456 797471520608 801499319936 814892974924 817799846416 825952646344 828898969696 830124295648 847006983788 855450955142 858502504328 877257233209 889163308054 899192248192 931306257056 934628395904 943945881536 968007981472 977658234448 981145719232 997541400338 1001099811992 1002579695096 1016186637776 1036853376706 1100735338304 1117323696512 1140047314672 1144114070848 1145805365824 1180763290196 1184975287664 1210862096542 1221128265931 1227295833652 1269251547347 1271127827711 1302911216768 1336123692736 1347451879648 1349443760224 1354257471616 1383842396048 1395575161064 1402623809888 1445417131102 1450573196968 1452717517384 1482262221629 1502379382574 1581534166912 1594943041216 1629785949848 1635599692832 1651905292688 1657797939392 1660248591296 1694013967576 1710901910284 1717005008656 1754514466418 1778326616108 1841838280969 1862612514112 1887891763072 1936015962944 1955316468896 1962291438464 1995082800676 2002199623984 2005159390192 2032373275552 2066335757843 2073706753412 2147767708891 2201470676608 2280094629344 2288228141696 2291610731648 2361526580392 2369950575328 2421724193084 2442256531862 2454591667304 2538503094694 2542255655422 2672247385472 2694903759296 2698887520448 2767684792096 2791150322128 2805247619776 2890834262204 2901146393936 2905435034768 2964524443258 2994078342997 3004758765148 3112071578189 3189886082432 3259571899696 3271199385664 3303810585376 3315595878784 3320497182592 3388027935152 3421803820568 3434010017312 3509028932836 3556653232216 3628986818471 3683676561938 3725225028224 3872031925888 3910632937792 3990165601352 4004399247968 4010318780384 4064746551104 4132671515686 4147413506824 4295535417782 4560189258688 4723053160784 4739901150656 4843448386168 4884513063724 4909183334608 5058959958857 5077006189388 5084511310844 5258327839009 5389807518592 5397775040896 5535369584192 5582300644256 5610495239552 5781668524408 5802292787872 5810870069536 5929048886516 5988156685994 6009517530296 6140800632463 6224143156378 6519143799392 6542398771328 6607621170752 6776055870304 6843607641136 6868020034624 7018057865672 7113306464432 7257973636942 7367353123876 7821265875584 7980331202704 8008798495936 8020637560768 8129493102208 8265343031372 8294827013648 8591070835564 8884760831429 8897894793977 9120378517376 9446106321568 9479802301312 9686896772336 9769026127448 9818366669216 10117919917714 10154012378776 10169022621688 10516655678018 11070739168384 11164601288512 11563337048816 11604585575744 11621740139072 11858097773032 11976313371988 12019035060592 12281601264926 12448286312756 12892867966783 13038287598784 13215242341504 13552111740608 13687215282272 13736040069248 14036115731344 14226612928864 14464350304901 14515947273884 14734706247752 15034373962237 15960662405408 16017596991872 16041275121536 16530686062744 16589654027296 17182141671128 17769521662858 17795789587954 18892212643136 19373793544672 19538052254896 19636733338432 20235839835428 20308024757552 20338045243376 20958548400979 21033311356036 21784501047323 22329202577024 23126674097632 23209171151488 23243480278144 23716195546064 23952626743976 24038070121184 24563202529852 24896572625512 25785735933566 26076575197568 27104223481216 27374430564544 28072231462688 28453225857728 28928700609802 29031894547768 29469412495504 30068747924474 31921324810816 33061372125488 33179308054592 34364283342256 35412719711999 35539043325716 35591579175908 36808294873063 37784425286272 38747587089344 39076104509792 39273466676864 40471679670856 40616049515104 40676090486752 41917096801958 42066622712072 42985604427241 43569002094646 46253348195264 47432391092128 47905253487952 48076140242368 49126405059704 49793145251024 51571471867132 54748861129088 56144462925376 56906451715456 57857401219604 58063789095536 58938824991008 60137495848948 62285263557839 63842649621632 66122744250976 66358616109184 68728566684512 70825439423998 71078086651432 71183158351816 73616589746126 77495174178688 78152209019584 80943359341712 81232099030208 81352180973504 83834193603916 84133245424144 85971208854482 87138004189292 90250075767481 92506696390528 94864782184256 95810506975904 96152280484736 98252810119408 99586290502048 103142943734264 105240617735659 112288925850752 115714802439208 116127578191072 117877649982016 120274991697896 124570527115678 132245488501952 137457133369024 141650878847996 142156173302864 142366316703632 146709838806853 147233179492252 152491507331261 156304418039168 161886718683424 162464198060416 162704361947008 167668387207832 168266490848288 171942417708964 174276008378584 180500151534962 189729564368512 191621013951808 196505620238816 199172581004096 206285887468528 210481235471318 231429604878416 232255156382144 235755299964032 240549983395792 249141054231356 257658064111441 264490977003904 274914266738048 283301757695992 284312346605728 284732633407264 293419677613706 294466358984504 304983014662522 323773437366848 335336774415664 336532981696576 343884835417928 348552016757168 361000303069924 383242027903616 393011240477632 398345162008192 412571774937056 420962470942636 435996844904873 462859209756832 464510312764288 481099966791584 498282108462712 515316128222882 566603515391984 568624693211456 569465266814528 586839355227412 588932717969008 609966029325044 631750530372367 647546874733696 670673548831328 673065963393152 687769670835856 697104033514336 722000606139848 786022480955264 825143549874112 841924941885272 871993689809746 925718419513664 962199933583168 996564216925424 1026968871647971 1030632256445764 1067440551318827 1133207030783968 1137249386422912 1138930533629056 1173678710454824 1177865435938016 1219932058650088 1263501060744734 1341347097662656 1375539341671712 1394208067028672 1444001212279696 1650287099748224 1683849883770544 1743987379619492 1851436839027328 1924399867166336 1993128433850848 2053937743295942 2061264512891528 2134881102637654 2266414061567936 2347357420909648 2355730871876032 2439864117300176 2527002121489468 2682694195325312 2751078683343424 2788416134057344 2888002424559392 3051977914334111 3367699767541088 3487974759238984 3986256867701696 4107875486591884 4122529025783056 4269762205275308 4422253712606569 4532828123135872 4694714841819296 4711461743752064 4879728234600352 5054004242978936 5502157366686848 5776004849118784 6103955828668222 6735399535082176 6975949518477968 7472083859231789 7972513735403392 8215750973183768 8245058051566112 8539524410550616 8844507425213138 9389429683638592 9759456469200704 10108008485957872 11552009698237568 12207911657336444 13470799070164352 13951899036955936 14944167718463578 16431501946367536 16490116103132224 17079048821101232 17689014850426276 18778859367277184 19518912938401408 20216016971915744 24415823314672888 27903798073911872 29888335436927156 30955775988245983 32863003892735072 32980232206264448 34158097642202464 35378029700852552 40432033943831488 48831646629345776 55807596147823744 59776670873854312 61911551976491966 65726007785470144 68316195284404928 70756059401705104 80864067887662976 97663293258691552 119553341747708624 123823103952983932 131452015570940288 136632390568809856 141512118803410208 195326586517383104 216690431917721881 239106683495417248 247646207905967864 283024237606820416 390653173034766208 433380863835443762 478213366990834496 495292415811935728 566048475213640832 866761727670887524 956426733981668992 990584831623871456 1733523455341775048 1981169663247742912 3467046910683550096 3962339326495485824 6934093821367100192 13868187642734200384 27736375285468400768
- Sum of all divisors σ(n): 68042337960639340800
- Sum of proper divisors (its aliquot sum) s(n): 40305962675170940032
- 27736375285468400768 is an abundant number, because the sum of its proper divisors (40305962675170940032) is greater than itself. Its abundance is 12569587389702539264
Bases of 27736375285468400768
- Binary: 110000000111010110110011001011110010101110100010010001100100000002
- Hexadecimal: 0x180EB665E57448C80
- Base-36: 5UQ7GGLZNVE68
Squares and roots of 27736375285468400768
- 27736375285468400768 squared (277363752854684007682) is 769306513976342310195279837039462989824
- 27736375285468400768 cubed (277363752854684007683) is 21337774181203271689174084667646552146270799410581137784832
-
The
square root of 27736375285468400768 is 5266533516.9794942421 -
The
cube root of 27736375285468400768 is 3027028.9067765829
Scales and comparisons
How big is 27736375285468400768?- 27,736,375,285,468,400,768 seconds is equal to 293,274,701,009 years, 3 weeks, 3 days, 15 hours, 30 minutes, 7 seconds.
-
To count from 1 to 27,736,375,285,468,400,768 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 27736375285468400768 cubic inches would be around 252252.4 feet tall.
Recreational maths with 27736375285468400768
- 27736375285468400768 backwards is 86700486458257363772
- 27736375285468400768 is a
Harshad number . - The number of decimal digits it has is: 20
- The sum of 27736375285468400768's digits is 98
- 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 27736375285468400768 - Facts about the integer". Numbermatics.com. 2024. Web. 19 June 2024.
APA style:
Numbermatics. (2024). Number 27736375285468400768 - Facts about the integer. Retrieved 19 June 2024, from https://numbermatics.com/n/27736375285468400768/
Chicago style:
Numbermatics. 2024. "Number 27736375285468400768 - Facts about the integer". https://numbermatics.com/n/27736375285468400768/
The information we have on file for 27736375285468400768 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 27736375285468400768, math, Factors of 27736375285468400768, curriculum, school, college, exams, university, Prime factorization of 27736375285468400768, STEM, science, technology, engineering, physics, economics, calculator, twenty-seven quintillion, seven hundred thirty-six quadrillion, three hundred seventy-five trillion, two hundred eighty-five billion, four hundred sixty-eight million, four hundred thousand, seven hundred sixty-eight.