962071919604224
962,071,919,604,224 is an even composite number composed of seven prime numbers multiplied together.
What does the number 962071919604224 look like?
This visualization shows the relationship between its 7 prime factors (large circles) and 2160 divisors.
962071919604224 is an even composite number. It is composed of seven distinct prime numbers multiplied together. It has a total of two thousand, one hundred sixty divisors.
Prime factorization of 962071919604224:
29 × 11 × 132 × 17 × 19 × 292 × 612
(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 11 × 13 × 13 × 17 × 19 × 29 × 29 × 61 × 61)See below for interesting mathematical facts about the number 962071919604224 from the Numbermatics database.
Names of 962071919604224
- Cardinal: 962071919604224 can be written as Nine hundred sixty-two trillion, seventy-one billion, nine hundred nineteen million, six hundred four thousand, two hundred twenty-four.
Scientific notation
- Scientific notation: 9.62071919604224 × 1014
Factors of 962071919604224
Divisors of 962071919604224
- Number of divisors d(n): 2160
-
Complete list of divisors:
1 2 4 8 11 13 16 17 19 22 26 29 32 34 38 44 52 58 61 64 68 76 88 104 116 122 128 136 143 152 169 176 187 208 209 221 232 244 247 256 272 286 304 319 323 338 352 374 377 416 418 442 464 488 493 494 512 544 551 572 608 638 646 671 676 704 748 754 793 832 836 841 884 928 976 986 988 1037 1088 1102 1144 1159 1216 1276 1292 1342 1352 1408 1496 1508 1586 1664 1672 1682 1768 1769 1856 1859 1952 1972 1976 2074 2176 2204 2288 2318 2431 2432 2552 2584 2684 2704 2717 2816 2873 2992 3016 3172 3211 3328 3344 3364 3536 3538 3553 3712 3718 3721 3904 3944 3952 4147 4148 4199 4352 4408 4576 4636 4862 4864 4901 5104 5168 5368 5408 5423 5434 5632 5746 5984 6032 6061 6344 6409 6422 6656 6688 6728 7072 7076 7106 7163 7424 7436 7442 7808 7888 7904 8294 8296 8398 8704 8723 8816 9152 9251 9272 9367 9724 9728 9802 10208 10309 10336 10736 10816 10846 10868 10933 11407 11492 11968 12064 12122 12688 12749 12818 12844 13376 13456 13481 14144 14152 14212 14297 14326 14848 14872 14884 15067 15616 15776 15808 15979 16588 16592 16796 17446 17632 18304 18502 18544 18734 19448 19459 19604 19703 20416 20618 20672 21472 21632 21692 21736 21866 22814 22984 22997 23936 24128 24244 25376 25498 25636 25688 26752 26912 26962 28288 28304 28424 28594 28652 29744 29768 30073 30134 31232 31552 31603 31616 31958 33176 33184 33592 33611 34892 35264 35321 36608 37004 37088 37468 38896 38918 39208 39406 40832 40931 41236 41344 42944 43264 43384 43472 43732 45628 45968 45994 46189 47872 48256 48373 48488 50752 50996 51272 51301 51376 53504 53824 53911 53924 54587 56576 56608 56848 57188 57304 59488 59536 60146 60268 63104 63206 63232 63257 63916 66352 66368 67184 67222 69784 70499 70528 70642 70699 73216 74008 74176 74936 77792 77836 78416 78793 78812 81664 81862 82472 82688 83317 85888 86528 86768 86944 87464 91256 91936 91988 92378 93119 95744 96512 96746 96976 101504 101992 102544 102602 102752 103037 107008 107648 107822 107848 107909 109174 113152 113216 113399 113696 114376 114608 118976 119072 120263 120292 120536 121771 126208 126412 126464 126514 127832 132704 132736 134368 134444 139568 140998 141056 141284 141398 142129 148016 148291 148352 149872 155584 155672 156832 157267 157586 157624 163328 163724 164944 165376 165737 166634 171776 173536 173888 174928 175253 175769 182512 183872 183976 184756 185861 186238 193024 193492 193952 195871 203008 203984 205088 205204 205504 206074 207727 215296 215644 215696 215818 216733 218348 226432 226798 227392 228752 229216 237952 238144 240526 240584 241072 243542 252416 252824 252967 253028 255664 256139 265408 265472 268736 268888 271643 279136 281996 282112 282568 282796 284258 296032 296582 296704 298961 299744 311168 311344 313664 314534 315172 315248 327448 329888 330803 331474 333268 343552 347072 347776 349856 350506 351538 365024 367744 367952 369512 369721 371722 372476 386984 387904 390949 391742 406016 407968 410176 410408 411008 412148 415454 430592 431288 431392 431636 433466 436696 436943 452864 453596 454784 457504 458432 475904 476288 481052 481168 482144 487084 505648 505934 506056 511328 512278 530816 530944 532103 537472 537776 543286 558272 563992 564311 565136 565592 568516 571387 592064 593164 593408 597922 599488 600457 622336 622688 627328 628849 629068 630344 630496 654896 659776 661606 662948 666536 666913 694144 695552 695827 699712 701012 703076 730048 735488 735904 739024 739442 743444 744952 773968 775808 777689 781898 783484 815936 820352 820816 822016 822341 824296 830908 862576 862784 863272 866932 872117 873392 873886 905728 907192 909568 915008 916487 916864 919087 951808 952576 962104 962336 964288 974168 974719 1011296 1011868 1012112 1022656 1024309 1024556 1061632 1064206 1074944 1075552 1086572 1116544 1127984 1128622 1130272 1131184 1137032 1142774 1184128 1186328 1186999 1195844 1198976 1200914 1201883 1244672 1245376 1254656 1257698 1258136 1260688 1260992 1309792 1319552 1323212 1325896 1333072 1333826 1339481 1388288 1391104 1391654 1399424 1402024 1402817 1406152 1460096 1470976 1471808 1478048 1478884 1486888 1489904 1547936 1551616 1555378 1563419 1563796 1566968 1583023 1631872 1640704 1641632 1644032 1644682 1648592 1661816 1725152 1725568 1726544 1733864 1744234 1746784 1747772 1814384 1819136 1830016 1832974 1833728 1834453 1838174 1905152 1924208 1924672 1927783 1928576 1948336 1949438 2022592 2023736 2024224 2044471 2045312 2048618 2049112 2050271 2123264 2128412 2149888 2151104 2154581 2173144 2233088 2255968 2257244 2260544 2262368 2274064 2284997 2285548 2368256 2372656 2373998 2391688 2397952 2401828 2403766 2416193 2490752 2509312 2515396 2516272 2521376 2521984 2619584 2639104 2646424 2651792 2666144 2667652 2678962 2700451 2776576 2783308 2798848 2804048 2805634 2812304 2817529 2920192 2943616 2956096 2957768 2973776 2979808 2988073 3095872 3103232 3110756 3126838 3127592 3129361 3133936 3166046 3263744 3281408 3283264 3288571 3289364 3297184 3323632 3329807 3450304 3451136 3453088 3467728 3488468 3493568 3495544 3531359 3628768 3660032 3665948 3667456 3668906 3676348 3848416 3849344 3855566 3857152 3896672 3898876 4045184 4047472 4048448 4088942 4090624 4097236 4098224 4100542 4256824 4300439 4302208 4309162 4346288 4466176 4511936 4514488 4521088 4524736 4548128 4569994 4571096 4736512 4745312 4747996 4783376 4795904 4803656 4806373 4807532 4832386 4981504 5030792 5032544 5042752 5043968 5082337 5239168 5278208 5292848 5303584 5332288 5335304 5357924 5400902 5566616 5597696 5608096 5611268 5624608 5635058 5680259 5840384 5887232 5912192 5915536 5947552 5959616 5976146 6191744 6221512 6253676 6255184 6258722 6267872 6285257 6332092 6527488 6566528 6577142 6578728 6594368 6647264 6659614 6900608 6902272 6906176 6917339 6935456 6976936 6987136 6991088 7062718 7257536 7320064 7331896 7336043 7337812 7352696 7428031 7696832 7698688 7711132 7714304 7793344 7797752 8090368 8094944 8096896 8177884 8181248 8194472 8196448 8201084 8513648 8600878 8604416 8618324 8669869 8692576 9023872 9028976 9042176 9045751 9049472 9096256 9139988 9142192 9490624 9495992 9566752 9593287 9607312 9612746 9615064 9664772 9963008 10061584 10065088 10085504 10087936 10109957 10164674 10478336 10585696 10607168 10664576 10670608 10690433 10715848 10721909 10801804 11133232 11216192 11222536 11249216 11270116 11337521 11360518 11774464 11824384 11831072 11895104 11919232 11948131 11952292 12383488 12443024 12507352 12510368 12517444 12535744 12570514 12664184 12671347 13133056 13154284 13157456 13188736 13220713 13294528 13319228 13801216 13812352 13834678 13870912 13953872 13974272 13982176 14125436 14515072 14663792 14672086 14675624 14705392 14856062 15393664 15397376 15422264 15430987 15586688 15595504 15624479 16180736 16189888 16193792 16355768 16388944 16392896 16402168 16570223 17027296 17201756 17208832 17236648 17339738 17385152 17413253 18047744 18057952 18084352 18091502 18098944 18192512 18236621 18279976 18284384 18981248 18991984 19133504 19186574 19214624 19225492 19230128 19329544 20123168 20130176 20171008 20178983 20219914 20329348 20956672 21171392 21214336 21329152 21341216 21380866 21431696 21443818 21603608 22266464 22432384 22445072 22498432 22540232 22552981 22675042 22721036 23648768 23662144 23790208 23838464 23847889 23896262 23904584 24766976 24886048 25014704 25020736 25034888 25071488 25141028 25328368 25342694 26266112 26308568 26314912 26377472 26441426 26578123 26589056 26638456 26653523 27602432 27624704 27669356 27741824 27907744 27948544 27964352 28250872 29030144 29327584 29344172 29351248 29410784 29704961 29712124 30787328 30844528 30861974 31173376 31191008 31248958 32379776 32387584 32711536 32777888 32785792 32804336 33140446 34054592 34403512 34422971 34473296 34679476 34770304 34826506 34854607 36095488 36115904 36183004 36197888 36385024 36473242 36559952 36568768 36627877 37962496 37983968 38267008 38373148 38429248 38450984 38460256 38659088 38844949 40246336 40260352 40342016 40357966 40439828 40658696 40681693 42342784 42428672 42658304 42682432 42761732 42863392 42887636 43207216 44532928 44864768 44890144 44996864 45080464 45105962 45350084 45442072 45907667 47324288 47580416 47676928 47695778 47792524 47809168 49772096 50029408 50041472 50069776 50142976 50282056 50656736 50685388 52617136 52629824 52754944 52882852 53156246 53178112 53199137 53276912 53307046 55249408 55338712 55483648 55815488 55905707 55928704 56501744 58060288 58655168 58688344 58702496 58821568 59409922 59424248 59457859 61574656 61689056 61723948 62346752 62382016 62482849 62497916 64759552 65423072 65555776 65571584 65608672 66280892 68109184 68807024 68845942 68946592 69358952 69540608 69653012 69709214 72231808 72366008 72770048 72946484 73119904 73137536 73255754 75924992 75967936 76534016 76746296 76858496 76901968 76920512 77318176 77689898 80492672 80520704 80715932 80879656 81317392 81363386 81708341 84685568 84857344 85364864 85523464 85726784 85775272 86414432 89065856 89729536 89780288 89993728 90160928 90211924 90700168 90884144 91815334 94648576 95160832 95368559 95391556 95585048 95618336 96564403 99544192 100058816 100082944 100139552 100285952 100564112 101313472 101370776 105234272 105259648 105765704 106312492 106356224 106398274 106553824 106614092 110677424 110967296 111630976 111811414 111857408 113003488 117310336 117376688 117404992 117594763 117643136 118819844 118848496 118915718 123378112 123447896 124712731 124764032 124965698 124995832 129519104 130846144 131111552 131143168 131217344 131429441 132561784 136218368 137614048 137691884 137893184 138717904 139081216 139306024 139384817 139418428 144463616 144732016 145892968 146239808 146275072 146511508 147387773 151935872 153068032 153492592 153716992 153803936 153841024 154636352 155379796 160985344 161431864 161759312 162634784 162726772 163416682 164727511 169371136 170729728 171046928 171453568 171550544 171869269 172828864 178131712 179560576 180321856 180423848 181400336 181768288 182272453 183630668 189297152 190737118 190783112 191170096 191236672 193128806 199088384 200117632 200165888 200279104 200602831 201128224 202626944 202741552 203118227 210468544 210519296 211531408 212624984 212796548 213107648 213228184 215412899 221354848 223261952 223622828 223714816 226006976 234620672 234753376 234809984 235189526 235286272 237639688 237696992 237831436 246756224 246895792 249425462 249528064 249931396 249991664 261692288 262223104 262326779 262434688 262858882 265123568 272436736 275228096 275383768 275786368 277435808 278612048 278769634 278836856 288927232 289464032 291785936 292479616 292550144 293023016 293188753 294775546 303871744 306985184 307433984 307607872 307682048 309272704 310022557 310759592 321970688 322863728 323518624 325269568 325453544 326833364 329455022 341459456 342093856 342907136 343101088 343738538 345657728 346495799 356263424 359121152 360643712 360847696 362800672 363536576 364544906 367261336 381474236 381566224 382340192 382473344 383400677 386257612 398176768 400235264 400558208 401205662 402256448 405253888 405483104 406236454 420937088 421038592 423062816 425249968 425593096 426215296 426456368 430825798 442709696 446523904 447245656 447498623 452013952 453109891 469241344 469506752 469619968 470379052 470572544 475279376 475393984 475662872 493512448 493791584 498850924 499056128 499862792 499983328 504984337 523384576 524446208 524653558 524869376 525717764 528862009 530247136 550456192 550767536 551572736 554871616 557224096 557539268 557673712 578928064 583571872 584959232 585190507 586046032 586377506 589551092 607743488 613970368 615215744 615364096 618545408 620045114 621519184 645727456 647037248 650539136 650907088 653666728 654036449 658910044 684187712 685814272 686202176 687477076 691315456 691588781 692991598 718242304 721287424 721695392 725601344 727073152 729089812 734522672 762948472 763132448 764680384 764946688 766801354 772515224 772952167 800470528 801116416 802411324 804512896 810507776 810966208 812472908 841874176 846125632 850499936 851186192 852430592 852912736 861651596 885419392 894491312 894997246 904027904 906219782 939013504 939239936 940758104 950558752 950787968 951325744 987024896 987583168 997701848 999725584 999966656 1009968674 1010783603 1046769152 1049307116 1049738752 1051435528 1057724018 1060494272 1062208433 1100912384 1101535072 1103145472 1109743232 1114448192 1115078536 1115347424 1157856128 1167143744 1169918464 1170381014 1172092064 1172755012 1179102184 1227940736 1230431488 1237090816 1240090228 1243038368 1291454912 1294074496 1301078272 1301814176 1307333456 1308072898 1317820088 1368375424 1372404352 1374954152 1382630912 1383177562 1385983196 1442574848 1443390784 1451202688 1454146304 1458179624 1469045344 1525896944 1526264896 1529360768 1529893376 1533602708 1545030448 1545904334 1602232832 1604822648 1609025792 1621265503 1621932416 1624945816 1683748352 1692251264 1700999872 1702372384 1704861184 1705825472 1723303192 1770838784 1788982624 1789994492 1808055808 1812002621 1812439564 1878027008 1881516208 1901117504 1901575936 1902651488 1975166336 1995403696 1999451168 1999933312 2019937348 2021567206 2098614232 2102871056 2115448036 2120988544 2124416866 2201824768 2203070144 2219486464 2228896384 2230157072 2230694848 2234300497 2315712256 2334287488 2340762028 2344184128 2345510024 2358204368 2369541889 2455881472 2460862976 2480180456 2486076736 2582909824 2588148992 2602156544 2603628352 2614666912 2616145796 2635640176 2736750848 2744808704 2749908304 2766355124 2771966392 2800367687 2886781568 2902405376 2908292608 2916359248 2938090688 3051793888 3052529792 3058721536 3067205416 3090060896 3091808668 3209645296 3218051584 3242531006 3243864832 3249891632 3384502528 3401999744 3404744768 3410248127 3411650944 3446606384 3541677568 3577965248 3579988984 3624005242 3624879128 3756054016 3763032416 3802235008 3803151872 3805302976 3811453789 3950332672 3990807392 3998902336 3999866624 4039874696 4043134412 4197228464 4205742112 4230896072 4241977088 4248833732 4406140288 4438972928 4457792768 4460314144 4461389696 4468600994 4631424512 4668574976 4681524056 4688368256 4691020048 4716408736 4739083778 4911762944 4960360912 4972153472 4984208801 5165819648 5176297984 5207256704 5229333824 5232291592 5271280352 5473501696 5489617408 5499816608 5532710248 5543932784 5600735374 5773563136 5804810752 5817482099 5832718496 5876181376 5890428583 6103587776 6105059584 6117443072 6134410832 6180121792 6183617336 6419290592 6485062012 6487729664 6499783264 6769005056 6803999488 6809489536 6820496254 6823301888 6893212768 7155930496 7159977968 7248010484 7249758256 7526064832 7604470016 7607476591 7610605952 7622907578 7900665344 7981614784 7997804672 7999733248 8079749392 8086268824 8394456928 8411484224 8461792144 8483954176 8497667464 8502473837 8812280576 8915585536 8920628288 8922779392 8937201988 8990654153 9337149952 9363048112 9376736512 9382040096 9432817472 9478167556 9920721824 9944306944 9968417602 10048378171 10331639296 10414513408 10458667648 10464583184 10542560704 10999633216 11065420496 11087865568 11118619633 11201470748 11547126272 11634964198 11665436992 11752362752 11780857166 12207175552 12210119168 12268821664 12360243584 12367234672 12838581184 12970124024 12999566528 13140186839 13607998976 13618979072 13640992508 13646603776 13786425536 14311860992 14319955936 14496020968 14499516512 15052129664 15208940032 15214953182 15221211904 15245815156 15963229568 15995609344 16159498784 16172537648 16788913856 16822968448 16923584288 16995334928 17004947674 17624561152 17841256576 17845558784 17874403976 17981308306 18726096224 18753473024 18764080192 18865634944 18956335112 19841443648 19888613888 19936835204 20096756342 20829026816 20917335296 20929166368 21085121408 21999266432 22130840992 22175731136 22237239266 22402941496 23269928396 23330873984 23504725504 23561714332 24414351104 24537643328 24720487168 24734469344 25677162368 25940248048 25999133056 26280373678 27237958144 27281985016 27572851072 28623721984 28639911872 28992041936 28999033024 30104259328 30429906364 30442423808 30491630312 30804044557 31926459136 31991218688 32318997568 32345075296 33577827712 33645936896 33847168576 33990669856 34009895348 35682513152 35748807952 35962616612 37452192448 37528160384 37731269888 37912670224 39682887296 39873670408 40193512684 41834670592 41858332736 42170242816 43998532864 44261681984 44351462272 44474478532 44805882992 46539856792 46661747968 47123428664 48828702208 49075286656 49440974336 49468938688 51354324736 51880496096 51998266112 52560747356 54563970032 55145702144 57279823744 57984083872 57998066048 60208518656 60859812728 60983260624 61608089114 63852918272 64637995136 64690150592 64794714413 67155655424 67291873792 67694337152 67981339712 68019790696 71365026304 71497615904 71925233224 74904384896 75056320768 75462539776 75825340448 79365774592 79747340816 80387025368 83716665472 84340485632 87997065728 88523363968 88702924544 88948957064 89611765984 93079713584 93323495936 94246857328 98150573312 98897195683 98937877376 102708649472 103760992192 103996532224 105121494712 109127940064 110291404288 110532159881 114559647488 115968167744 115996132096 121719625456 121966521248 123216178228 129275990272 129380301184 129589428826 134311310848 135388674304 135962679424 136039581392 142995231808 143850466448 144542055229 149808769792 150112641536 151650680896 158731549184 159494681632 160774050736 167433330944 170822428907 177046727936 177405849088 177897914128 179223531968 186159427168 188493714656 196301146624 197794391366 197875754752 207521984384 210242989424 218255880128 221064319762 229119294976 231936335488 231992264192 243439250912 243933042496 246432356456 258551980544 258760602368 259178857652 270777348608 271925358848 272079162784 285990463616 287700932896 289084110458 299617539584 303301361792 318989363264 321548101472 334866661888 341644857814 354093455872 355795828256 358447063936 372318854336 376987429312 395588782732 395751509504 415043968768 420485978848 436511760256 442128639524 463872670976 486878501824 487866084992 492864712912 517521204736 518357715304 543850717696 544158325568 571980927232 575401865792 578168220916 606602723584 637978726528 643096202944 683289715628 711591656512 716894127872 744637708672 753974858624 791177565464 830087937536 840971957696 873023520512 884257279048 927745341952 973757003648 975732169984 985729425824 1036715430608 1088316651136 1143961854464 1150803731584 1156336441832 1213205447168 1275957453056 1286192405888 1366579431256 1423183313024 1433788255744 1489275417344 1507949717248 1582355130928 1681943915392 1746047041024 1768514558096 1879046717977 1947514007296 1951464339968 1971458851648 2073430861216 2176633302272 2301607463168 2312672883664 2551914906112 2572384811776 2733158862512 2846366626048 2978550834688 3015899434496 3164710261856 3363887830784 3537029116192 3758093435954 3895028014592 3942917703296 4146861722432 4353266604544 4603214926336 4625345767328 5144769623552 5466317725024 5692733252096 6329420523712 6727775661568 7074058232384 7516186871908 7885835406592 8293723444864 9250691534656 10932635450048 12658841047424 14148116464768 15032373743816 15771670813184 16587446889728 18501383069312 21865270900096 25317682094848 28296232929536 30064747487632 33174893779456 37002766138624 43730541800192 50635364189696 56592465859072 60129494975264 74005532277248 87461083600384 120258989950528 240517979901056 481035959802112 962071919604224
- Sum of all divisors σ(n): 2664802128399840
- Sum of proper divisors (its aliquot sum) s(n): 1702730208795616
- 962071919604224 is an abundant number, because the sum of its proper divisors (1702730208795616) is greater than itself. Its abundance is 740658289191392
Bases of 962071919604224
- Binary: 110110101011111111110100110000010000110010000000002
- Hexadecimal: 0x36AFFD3043200
- Base-36: 9H0XQKYZ28
Squares and roots of 962071919604224
- 962071919604224 squared (9620719196042242) is 925582378490956447736798642176
- 962071919604224 cubed (9620719196042243) is 890476815626637880880884745272178078514151424
-
The
square root of 962071919604224 is 31017284.2074257687 -
The
cube root of 962071919604224 is 98719.4013270619
Scales and comparisons
How big is 962071919604224?- 962,071,919,604,224 seconds is equal to 30,590,911 years, 8 weeks, 2 days, 2 hours, 3 minutes, 44 seconds.
-
To count from 1 to 962,071,919,604,224 would take you about seventy-six million, four hundred seventy-seven thousand, two hundred seventy-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 962071919604224 cubic inches would be around 8226.6 feet tall.
Recreational maths with 962071919604224
- 962071919604224 backwards is 422406919170269
- The number of decimal digits it has is: 15
- The sum of 962071919604224's digits is 62
- 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 962071919604224 - Facts about the integer". Numbermatics.com. 2024. Web. 20 June 2024.
APA style:
Numbermatics. (2024). Number 962071919604224 - Facts about the integer. Retrieved 20 June 2024, from https://numbermatics.com/n/962071919604224/
Chicago style:
Numbermatics. 2024. "Number 962071919604224 - Facts about the integer". https://numbermatics.com/n/962071919604224/
The information we have on file for 962071919604224 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 962071919604224, math, Factors of 962071919604224, curriculum, school, college, exams, university, Prime factorization of 962071919604224, STEM, science, technology, engineering, physics, economics, calculator, nine hundred sixty-two trillion, seventy-one billion, nine hundred nineteen million, six hundred four thousand, two hundred twenty-four.