44109329615290368
44,109,329,615,290,368 is an even composite number composed of five prime numbers multiplied together.
44109329615290368 is an even composite number. It is composed of five distinct prime numbers multiplied together. It has a total of two thousand divisors.
Prime factorization of 44109329615290368:
224 × 34 × 11 × 13 × 613
(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 11 × 13 × 61 × 61 × 61)See below for interesting mathematical facts about the number 44109329615290368 from the Numbermatics database.
Names of 44109329615290368
- Cardinal: 44109329615290368 can be written as Forty-four quadrillion, one hundred nine trillion, three hundred twenty-nine billion, six hundred fifteen million, two hundred ninety thousand, three hundred sixty-eight.
Scientific notation
- Scientific notation: 4.4109329615290368 × 1016
Factors of 44109329615290368
Divisors of 44109329615290368
- Number of divisors d(n): 2000
-
Complete list of divisors:
1 2 3 4 6 8 9 11 12 13 16 18 22 24 26 27 32 33 36 39 44 48 52 54 61 64 66 72 78 81 88 96 99 104 108 117 122 128 132 143 144 156 162 176 183 192 198 208 216 234 244 256 264 286 288 297 312 324 351 352 366 384 396 416 429 432 468 488 512 528 549 572 576 594 624 648 671 702 704 732 768 792 793 832 858 864 891 936 976 1024 1053 1056 1098 1144 1152 1188 1248 1287 1296 1342 1404 1408 1464 1536 1584 1586 1647 1664 1716 1728 1782 1872 1952 2013 2048 2106 2112 2196 2288 2304 2376 2379 2496 2574 2592 2684 2808 2816 2928 3072 3168 3172 3294 3328 3432 3456 3564 3721 3744 3861 3904 4026 4096 4212 4224 4392 4576 4608 4752 4758 4941 4992 5148 5184 5368 5616 5632 5856 6039 6144 6336 6344 6588 6656 6864 6912 7128 7137 7442 7488 7722 7808 8052 8192 8424 8448 8723 8784 9152 9216 9504 9516 9882 9984 10296 10368 10736 11163 11232 11264 11583 11712 12078 12288 12672 12688 13176 13312 13728 13824 14256 14274 14884 14976 15444 15616 16104 16384 16848 16896 17446 17568 18117 18304 18432 19008 19032 19764 19968 20592 20736 21411 21472 22326 22464 22528 23166 23424 24156 24576 25344 25376 26169 26352 26624 27456 27648 28512 28548 29768 29952 30888 31232 32208 32768 33489 33696 33792 34892 35136 36234 36608 36864 38016 38064 39528 39936 40931 41184 41472 42822 42944 44652 44928 45056 46332 46848 48312 48373 49152 50688 50752 52338 52704 53248 54351 54912 55296 57024 57096 59536 59904 61776 62464 64233 64416 65536 66978 67392 67584 69784 70272 72468 73216 73728 76032 76128 78507 79056 79872 81862 82368 82944 85644 85888 89304 89856 90112 92664 93696 96624 96746 98304 100467 101376 101504 104676 105408 106496 108702 109824 110592 114048 114192 119072 119808 122793 123552 124928 128466 128832 131072 133956 134784 135168 139568 140544 144936 145119 146432 147456 152064 152256 157014 158112 159744 163724 164736 165888 171288 171776 178608 179712 180224 185328 187392 193248 193492 196608 200934 202752 203008 209352 210816 212992 217404 219648 221184 226981 228096 228384 235521 238144 239616 245586 247104 249856 256932 257664 262144 267912 269568 270336 279136 281088 289872 290238 292864 294912 301401 304128 304512 314028 316224 319488 327448 329472 331776 342576 343552 357216 359424 360448 368379 370656 374784 386496 386984 393216 401868 405504 406016 418704 421632 425984 434808 435357 439296 442368 453962 456192 456768 471042 476288 479232 491172 494208 499712 513864 515328 524288 532103 535824 539136 540672 558272 562176 579744 580476 585728 589824 602802 608256 609024 628056 632448 638976 654896 658944 663552 680943 685152 687104 706563 714432 718848 720896 736758 741312 749568 772992 773968 786432 803736 811008 812032 837408 843264 851968 869616 870714 878592 884736 907924 912384 913536 942084 952576 958464 982344 988416 999424 1027728 1030656 1048576 1064206 1071648 1078272 1081344 1105137 1116544 1124352 1159488 1160952 1171456 1179648 1205604 1216512 1218048 1256112 1264896 1277952 1306071 1309792 1317888 1327104 1361886 1370304 1374208 1413126 1428864 1437696 1441792 1473516 1482624 1499136 1545984 1547936 1572864 1596309 1607472 1622016 1624064 1674816 1686528 1703936 1739232 1741428 1757184 1769472 1815848 1824768 1827072 1884168 1905152 1916928 1964688 1976832 1998848 2042829 2055456 2061312 2097152 2128412 2143296 2156544 2162688 2210274 2233088 2248704 2318976 2321904 2342912 2359296 2411208 2433024 2436096 2496791 2512224 2529792 2555904 2612142 2619584 2635776 2654208 2723772 2740608 2748416 2826252 2857728 2875392 2883584 2947032 2950753 2965248 2998272 3091968 3095872 3145728 3192618 3214944 3244032 3248128 3315411 3349632 3373056 3407872 3478464 3482856 3514368 3538944 3631696 3649536 3654144 3768336 3810304 3833856 3918213 3929376 3953664 3997696 4085658 4110912 4122624 4194304 4256824 4286592 4313088 4325376 4420548 4466176 4497408 4637952 4643808 4685824 4718592 4788927 4822416 4866048 4872192 4993582 5024448 5059584 5111808 5224284 5239168 5271552 5308416 5447544 5481216 5496832 5652504 5715456 5750784 5767168 5894064 5901506 5930496 5996544 6128487 6183936 6191744 6291456 6385236 6429888 6488064 6496256 6630822 6699264 6746112 6815744 6956928 6965712 7028736 7077888 7263392 7299072 7308288 7490373 7536672 7620608 7667712 7836426 7858752 7907328 7995392 8171316 8221824 8245248 8388608 8513648 8573184 8626176 8650752 8841096 8852259 8932352 8994816 9275904 9287616 9371648 9437184 9577854 9644832 9732096 9744384 9987164 10048896 10119168 10223616 10448568 10478336 10543104 10616832 10895088 10962432 10993664 11305008 11430912 11501568 11534336 11788128 11803012 11860992 11993088 12256974 12367872 12383488 12582912 12770472 12859776 12976128 12992512 13261644 13398528 13492224 13631488 13913856 13931424 14057472 14155776 14366781 14526784 14598144 14616576 14980746 15073344 15241216 15335424 15672852 15717504 15814656 15990784 16342632 16443648 16490496 16777216 17027296 17146368 17252352 17301504 17682192 17704518 17864704 17989632 18385461 18551808 18575232 18743296 18874368 19155708 19289664 19464192 19488768 19974328 20097792 20238336 20447232 20897136 20956672 21086208 21233664 21790176 21924864 21987328 22471119 22610016 22861824 23003136 23068672 23576256 23606024 23721984 23986176 24513948 24735744 24766976 25165824 25540944 25719552 25952256 25985024 26523288 26556777 26797056 26984448 27262976 27827712 27862848 28114944 28311552 28733562 29053568 29196288 29233152 29961492 30146688 30482432 30670848 31345704 31435008 31629312 31981568 32458283 32685264 32887296 32980992 34054592 34292736 34504704 34603008 35364384 35409036 35729408 35979264 36770922 37103616 37150464 37486592 37748736 38311416 38579328 38928384 38977536 39948656 40195584 40476672 40894464 41794272 41913344 42172416 42467328 43100343 43580352 43849728 43974656 44942238 45220032 45723648 46006272 46137344 47152512 47212048 47443968 47972352 49027896 49471488 49533952 50331648 51081888 51439104 51904512 51970048 53046576 53113554 53594112 53968896 54525952 55655424 55725696 56229888 56623104 57467124 58107136 58392576 58466304 59922984 60293376 60964864 61341696 62691408 62870016 63258624 63963136 64916566 65370528 65774592 65961984 67413357 68109184 68585472 69009408 69206016 70728768 70818072 71458816 71958528 73541844 74207232 74300928 74973184 75497472 76622832 77158656 77856768 77955072 79670331 79897312 80391168 80953344 81788928 83588544 83826688 84344832 84934656 86200686 87160704 87699456 87949312 89884476 90440064 91447296 92012544 92274688 94305024 94424096 94887936 95944704 97374849 98055792 98942976 99067904 102163776 102878208 103809024 103940096 106093152 106227108 107188224 107937792 109051904 111310848 111451392 112459776 113246208 114934248 116214272 116785152 116932608 119845968 120586752 121929728 122683392 125382816 125740032 126517248 127926272 129833132 130741056 131549184 131923968 134826714 136218368 137170944 138018816 138412032 141457536 141636144 142917632 143917056 147083688 148414464 148601856 149946368 150994944 153245664 154317312 155713536 155910144 159340662 159794624 160782336 161906688 163577856 167177088 167653376 168689664 169869312 172401372 174321408 175398912 175898624 179768952 180880128 182894592 184025088 184549376 188610048 188848192 189775872 191889408 194749698 196111584 197885952 198135808 202240071 204327552 205756416 207618048 207880192 212186304 212454216 214376448 215875584 218103808 222621696 222902784 224919552 226492416 229868496 232428544 233570304 233865216 239010993 239691936 241173504 243859456 245366784 250765632 251480064 253034496 255852544 259666264 261482112 263098368 263847936 269653428 272436736 274341888 276037632 276824064 282915072 283272288 285835264 287834112 292124547 294167376 296828928 297203712 299892736 306491328 308634624 311427072 311820288 318681324 319589248 321564672 323813376 327155712 334354176 335306752 337379328 339738624 344802744 348642816 350797824 351797248 359537904 361760256 365789184 368050176 377220096 377696384 379551744 383778816 389499396 392223168 395771904 396271616 404480142 408655104 411512832 415236096 415760384 424372608 424908432 428752896 431751168 445243392 445805568 449839104 452984832 459736992 464857088 467140608 467730432 478021986 479383872 482347008 487718912 490733568 501531264 502960128 506068992 511705088 519332528 522964224 526196736 527695872 539306856 544873472 548683776 552075264 553648128 565830144 566544576 571670528 575668224 584249094 588334752 593657856 594407424 599785472 612982656 617269248 622854144 623640576 637362648 639178496 643129344 647626752 654311424 668708352 670613504 674758656 679477248 689605488 697285632 701595648 703594496 719075808 723520512 731578368 736100352 754440192 755392768 759103488 767557632 778998792 784446336 791543808 792543232 808960284 817310208 823025664 830472192 831520768 848745216 849816864 857505792 863502336 876373641 890486784 891611136 899678208 919473984 929714176 934281216 935460864 956043972 958767744 964694016 975437824 981467136 1003062528 1005920256 1012137984 1023410176 1038665056 1045928448 1052393472 1055391744 1078613712 1089746944 1097367552 1104150528 1131660288 1133089152 1143341056 1151336448 1168498188 1176669504 1187315712 1188814848 1199570944 1225965312 1234538496 1245708288 1247281152 1274725296 1278356992 1286258688 1295253504 1337416704 1341227008 1349517312 1358954496 1379210976 1394571264 1403191296 1407188992 1438151616 1447041024 1463156736 1472200704 1508880384 1510785536 1518206976 1535115264 1557997584 1568892672 1583087616 1585086464 1617920568 1634620416 1646051328 1660944384 1663041536 1697490432 1699633728 1715011584 1727004672 1752747282 1780973568 1783222272 1799356416 1838947968 1859428352 1868562432 1870921728 1912087944 1917535488 1929388032 1950875648 1962934272 2006125056 2011840512 2024275968 2077330112 2091856896 2104786944 2110783488 2157227424 2179493888 2194735104 2208301056 2263320576 2266178304 2286682112 2302672896 2336996376 2353339008 2374631424 2377629696 2399141888 2451930624 2469076992 2491416576 2494562304 2549450592 2556713984 2572517376 2590507008 2629120923 2674833408 2682454016 2699034624 2758421952 2789142528 2806382592 2814377984 2876303232 2894082048 2926313472 2944401408 3017760768 3021571072 3036413952 3070230528 3115995168 3137785344 3166175232 3170172928 3235841136 3269240832 3292102656 3326083072 3394980864 3399267456 3430023168 3454009344 3505494564 3561947136 3566444544 3598712832 3677895936 3718856704 3737124864 3741843456 3824175888 3835070976 3858776064 3901751296 4012250112 4023681024 4048551936 4154660224 4183713792 4209573888 4221566976 4314454848 4358987776 4389470208 4416602112 4526641152 4532356608 4573364224 4605345792 4673992752 4706678016 4749262848 4755259392 4903861248 4938153984 4982833152 4989124608 5098901184 5113427968 5145034752 5181014016 5258241846 5349666816 5364908032 5398069248 5516843904 5578285056 5612765184 5628755968 5752606464 5788164096 5852626944 5888802816 6035521536 6043142144 6072827904 6231990336 6275570688 6332350464 6340345856 6471682272 6538481664 6584205312 6652166144 6789961728 6798534912 6860046336 6908018688 7010989128 7123894272 7132889088 7197425664 7355791872 7437713408 7474249728 7483686912 7648351776 7670141952 7717552128 7803502592 8024500224 8047362048 8097103872 8309320448 8367427584 8419147776 8443133952 8628909696 8717975552 8778940416 8833204224 9053282304 9064713216 9146728448 9210691584 9347985504 9413356032 9498525696 9510518784 9807722496 9876307968 9978249216 10197802368 10226855936 10290069504 10362028032 10516483692 10699333632 10729816064 10796138496 11033687808 11156570112 11225530368 11257511936 11505212928 11576328192 11705253888 12071043072 12086284288 12145655808 12463980672 12551141376 12664700928 12680691712 12943364544 13076963328 13168410624 13304332288 13579923456 13597069824 13720092672 13816037376 14021978256 14247788544 14265778176 14711583744 14875426816 14948499456 14967373824 15296703552 15340283904 15435104256 15607005184 16049000448 16094724096 16194207744 16618640896 16734855168 16838295552 16886267904 17257819392 17435951104 17557880832 17666408448 18106564608 18129426432 18293456896 18695971008 18826712064 18997051392 19021037568 19615444992 19752615936 19956498432 20395604736 20453711872 20580139008 20724056064 21032967384 21398667264 21459632128 21592276992 22067375616 22313140224 22451060736 23010425856 23152656384 23410507776 24142086144 24172568576 24291311616 24927961344 25102282752 25329401856 25361383424 25886729088 26153926656 26336821248 27159846912 27194139648 27440185344 27632074752 28043956512 28495577088 28531556352 29423167488 29750853632 29934747648 30593407104 30680567808 30870208512 31214010368 32098000896 32189448192 32388415488 33237281792 33469710336 33676591104 33772535808 34515638784 34871902208 35115761664 36213129216 36258852864 36586913792 37391942016 37653424128 37994102784 38042075136 39230889984 39505231872 39912996864 40791209472 40907423744 41160278016 41448112128 42065934768 42797334528 42919264256 44134751232 44626280448 44902121472 46020851712 46305312768 46821015552 48284172288 48345137152 48582623232 49855922688 50204565504 50658803712 50722766848 51773458176 52307853312 52673642496 54319693824 54388279296 54880370688 56087913024 56991154176 57063112704 58846334976 59501707264 59869495296 61186814208 61361135616 61740417024 62428020736 64196001792 64378896384 64776830976 66474563584 66939420672 67353182208 69031277568 69743804416 70231523328 72426258432 72517705728 73173827584 74783884032 75306848256 75988205568 76084150272 78461779968 79010463744 81582418944 81814847488 82320556032 82896224256 84131869536 85594669056 85838528512 88269502464 89252560896 89804242944 92041703424 92610625536 93642031104 96568344576 96690274304 97165246464 99711845376 100409131008 101317607424 101445533696 103546916352 104615706624 105347284992 108639387648 108776558592 109760741376 112175826048 113982308352 114126225408 117692669952 119003414528 119738990592 122373628416 122722271232 123480834048 128392003584 128757792768 132949127168 133878841344 134706364416 138062555136 139487608832 140463046656 144852516864 145035411456 146347655168 149567768064 150613696512 151976411136 152168300544 156923559936 158020927488 163164837888 163629694976 164641112064 168263739072 171189338112 171677057024 176539004928 178505121792 179608485888 184083406848 185221251072 187284062208 193136689152 193380548608 194330492928 199423690752 200818262016 202891067392 207093832704 209231413248 210694569984 217278775296 217553117184 219521482752 224351652096 227964616704 228252450816 235385339904 238006829056 244747256832 245444542464 246961668096 256784007168 257515585536 265898254336 267757682688 269412728832 276125110272 278975217664 280926093312 289705033728 290070822912 299135536128 301227393024 303952822272 304336601088 313847119872 316041854976 326329675776 327259389952 329282224128 336527478144 342378676224 343354114048 353078009856 357010243584 359216971776 368166813696 370442502144 386273378304 386761097216 398847381504 401636524032 405782134784 414187665408 418462826496 421389139968 434557550592 435106234368 439042965504 448703304192 455929233408 456504901632 470770679808 476013658112 489494513664 490889084928 493923336192 513568014336 515031171072 531796508672 535515365376 538825457664 552250220544 557950435328 561852186624 579410067456 580141645824 598271072256 602454786048 608673202176 627694239744 632083709952 652659351552 654518779904 658564448256 673054956288 684757352448 686708228096 706156019712 714020487168 736333627392 740885004288 772546756608 773522194432 797694763008 803273048064 811564269568 828375330816 836925652992 842778279936 869115101184 870212468736 897406608384 911858466816 913009803264 941541359616 952027316224 978989027328 981778169856 987846672384 1027136028672 1030062342144 1063593017344 1071030730752 1077650915328 1104500441088 1115900870656 1158820134912 1160283291648 1196542144512 1204909572096 1217346404352 1255388479488 1264167419904 1305318703104 1309037559808 1317128896512 1346109912576 1369514704896 1412312039424 1428040974336 1472667254784 1481770008576 1545093513216 1547044388864 1595389526016 1606546096128 1656750661632 1673851305984 1685556559872 1738230202368 1740424937472 1794813216768 1826019606528 1883082719232 1904054632448 1957978054656 1963556339712 1975693344768 2054272057344 2060124684288 2127186034688 2142061461504 2209000882176 2231801741312 2317640269824 2320566583296 2393084289024 2409819144192 2434692808704 2510776958976 2528334839808 2610637406208 2618075119616 2692219825152 2739029409792 2824624078848 2856081948672 2945334509568 2963540017152 3090187026432 3094088777728 3190779052032 3213092192256 3313501323264 3347702611968 3476460404736 3480849874944 3589626433536 3652039213056 3766165438464 3808109264896 3915956109312 3927112679424 3951386689536 4108544114688 4254372069376 4284122923008 4418001764352 4463603482624 4635280539648 4641133166592 4786168578048 4819638288384 5021553917952 5056669679616 5221274812416 5236150239232 5384439650304 5478058819584 5649248157696 5712163897344 5890669019136 5927080034304 6180374052864 6188177555456 6381558104064 6426184384512 6627002646528 6695405223936 6952920809472 6961699749888 7179252867072 7304078426112 7532330876928 7831912218624 7854225358848 8217088229376 8508744138752 8568245846016 8836003528704 8927206965248 9270561079296 9282266333184 9572337156096 9639276576768 10043107835904 10442549624832 10472300478464 10768879300608 10956117639168 11298496315392 11424327794688 11781338038272 11854160068608 12376355110912 12763116208128 12852368769024 13254005293056 13390810447872 13905841618944 13923399499776 14358505734144 15064661753856 15663824437248 15708450717696 16434176458752 17017488277504 17136491692032 17672007057408 18541122158592 18564532666368 19144674312192 19278553153536 20086215671808 20885099249664 20944600956928 21537758601216 21912235278336 22596992630784 23562676076544 24752710221824 25526232416256 25704737538048 26508010586112 26781620895744 27811683237888 27846798999552 28717011468288 30129323507712 31327648874496 31416901435392 32868352917504 34034976555008 34272983384064 35344014114816 37129065332736 38289348624384 38557106307072 40172431343616 41770198499328 41889201913856 43075517202432 45193985261568 47125352153088 49505420443648 51052464832512 51409475076096 53016021172224 55623366475776 55693597999104 57434022936576 60258647015424 62655297748992 62833802870784 65736705835008 68069953110016 70688028229632 74258130665472 76578697248768 77114212614144 80344862687232 83540396998656 86151034404864 90387970523136 94250704306176 102104929665024 102818950152192 106032042344448 111387195998208 114868045873152 120517294030848 125310595497984 125667605741568 136139906220032 141376056459264 148516261330944 153157394497536 154228425228288 167080793997312 172302068809728 180775941046272 188501408612352 204209859330048 212064084688896 222774391996416 229736091746304 241034588061696 250621190995968 272279812440064 282752112918528 306314788995072 308456850456576 334161587994624 344604137619456 361551882092544 377002817224704 408419718660096 424128169377792 445548783992832 459472183492608 501242381991936 544559624880128 565504225837056 612629577990144 668323175989248 689208275238912 723103764185088 816839437320192 848256338755584 918944366985216 1002484763983872 1131008451674112 1225259155980288 1336646351978496 1378416550477824 1633678874640384 1696512677511168 1837888733970432 2004969527967744 2450518311960576 2756833100955648 3393025355022336 3675777467940864 4009939055935488 4901036623921152 5513666201911296 7351554935881728 11027332403822592 14703109871763456 22054664807645184 44109329615290368
- Sum of all divisors σ(n): 157402849052293152
- Sum of proper divisors (its aliquot sum) s(n): 113293519437002784
- 44109329615290368 is an abundant number, because the sum of its proper divisors (113293519437002784) is greater than itself. Its abundance is 69184189821712416
Bases of 44109329615290368
- Binary: 100111001011010100110011100110110000000000000000000000002
- Hexadecimal: 0x9CB5339B000000
- Base-36: C2BGAA7SW00
Squares and roots of 44109329615290368
- 44109329615290368 squared (441093296152903682) is 1945632959110331923868380953575424
- 44109329615290368 cubed (441093296152903683) is 85820565503770397533038450217716204020109548716032
-
The
square root of 44109329615290368 is 210022212.1950208579 -
The
cube root of 44109329615290368 is 353326.9944289037
Scales and comparisons
How big is 44109329615290368?- 44,109,329,615,290,368 seconds is equal to 1,402,540,242 years, 33 weeks, 6 days, 2 hours, 52 minutes, 48 seconds.
-
To count from 1 to 44,109,329,615,290,368 would take you about four billion, two hundred seven million, six hundred twenty thousand, seven hundred twenty-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 44109329615290368 cubic inches would be around 29443.9 feet tall.
Recreational maths with 44109329615290368
- 44109329615290368 backwards is 86309251692390144
- 44109329615290368 is a
Harshad number . - The number of decimal digits it has is: 17
- The sum of 44109329615290368's digits is 72
- 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 44109329615290368 - Facts about the integer". Numbermatics.com. 2024. Web. 26 May 2024.
APA style:
Numbermatics. (2024). Number 44109329615290368 - Facts about the integer. Retrieved 26 May 2024, from https://numbermatics.com/n/44109329615290368/
Chicago style:
Numbermatics. 2024. "Number 44109329615290368 - Facts about the integer". https://numbermatics.com/n/44109329615290368/
The information we have on file for 44109329615290368 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 44109329615290368, math, Factors of 44109329615290368, curriculum, school, college, exams, university, Prime factorization of 44109329615290368, STEM, science, technology, engineering, physics, economics, calculator, forty-four quadrillion, one hundred nine trillion, three hundred twenty-nine billion, six hundred fifteen million, two hundred ninety thousand, three hundred sixty-eight.