32418385171907979024
32,418,385,171,907,979,024 is an even composite number composed of four prime numbers multiplied together.
32418385171907979024 is an even composite number. It is composed of four distinct prime numbers multiplied together. It has a total of one thousand, seven hundred eighty-five divisors.
Prime factorization of 32418385171907979024:
24 × 316 × 116 × 1632
(2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 11 × 11 × 11 × 11 × 11 × 11 × 163 × 163)See below for interesting mathematical facts about the number 32418385171907979024 from the Numbermatics database.
Names of 32418385171907979024
- Cardinal: 32418385171907979024 can be written as Thirty-two quintillion, four hundred eighteen quadrillion, three hundred eighty-five trillion, one hundred seventy-one billion, nine hundred seven million, nine hundred seventy-nine thousand and twenty-four.
Scientific notation
- Scientific notation: 3.2418385171907979024 × 1019
Factors of 32418385171907979024
Divisors of 32418385171907979024
- Number of divisors d(n): 1785
-
Complete list of divisors:
1 2 3 4 6 8 9 11 12 16 18 22 24 27 33 36 44 48 54 66 72 81 88 99 108 121 132 144 162 163 176 198 216 242 243 264 297 324 326 363 396 432 484 486 489 528 594 648 652 726 729 792 891 968 972 978 1089 1188 1296 1304 1331 1452 1458 1467 1584 1782 1793 1936 1944 1956 2178 2187 2376 2608 2662 2673 2904 2916 2934 3267 3564 3586 3888 3912 3993 4356 4374 4401 4752 5324 5346 5379 5808 5832 5868 6534 6561 7128 7172 7824 7986 8019 8712 8748 8802 9801 10648 10692 10758 11664 11736 11979 13068 13122 13203 14256 14344 14641 15972 16038 16137 17424 17496 17604 19602 19683 19723 21296 21384 21516 23472 23958 24057 26136 26244 26406 26569 28688 29282 29403 31944 32076 32274 34992 35208 35937 39204 39366 39446 39609 42768 43032 43923 47916 48114 48411 52272 52488 52812 53138 58564 58806 59049 59169 63888 64152 64548 70416 71874 72171 78408 78732 78892 79218 79707 86064 87846 88209 95832 96228 96822 104976 105624 106276 107811 117128 117612 118098 118338 118827 128304 129096 131769 143748 144342 145233 156816 157464 157784 158436 159414 161051 175692 176418 177147 177507 191664 192456 193644 211248 212552 215622 216513 216953 234256 235224 236196 236676 237654 239121 258192 263538 264627 287496 288684 290466 292259 314928 315568 316872 318828 322102 323433 351384 352836 354294 355014 356481 384912 387288 395307 425104 431244 433026 433906 435699 470448 472392 473352 475308 478242 483153 527076 529254 531441 532521 574992 577368 580932 584518 633744 637656 644204 646866 649539 650859 702768 705672 708588 710028 712962 717363 774576 790614 793881 862488 866052 867812 871398 876777 944784 946704 950616 956484 966306 970299 1054152 1058508 1062882 1065042 1069443 1154736 1161864 1169036 1185921 1275312 1288408 1293732 1299078 1301718 1307097 1411344 1417176 1420056 1425924 1434726 1449459 1581228 1587762 1594323 1597563 1724976 1732104 1735624 1742796 1753554 1771561 1901232 1912968 1932612 1940598 1948617 1952577 2108304 2117016 2125764 2130084 2138886 2152089 2323728 2338072 2371842 2381643 2386483 2576816 2587464 2598156 2603436 2614194 2630331 2834352 2840112 2851848 2869452 2898918 2910897 3162456 3175524 3188646 3195126 3208329 3214849 3464208 3471248 3485592 3507108 3543122 3557763 3825936 3865224 3881196 3897234 3905154 3921291 4234032 4251528 4260168 4277772 4304178 4348377 4676144 4743684 4763286 4772966 4782969 4792689 5174928 5196312 5206872 5228388 5260662 5314683 5703696 5738904 5797836 5821794 5845851 5857731 6324912 6351048 6377292 6390252 6416658 6429698 6456267 6971184 7014216 7086244 7115526 7144929 7159449 7730448 7762392 7794468 7810308 7842582 7890993 8503056 8520336 8555544 8608356 8696754 8732691 9487368 9526572 9545932 9565938 9585378 9624987 9644547 10392624 10413744 10456776 10521324 10629366 10673289 11477808 11595672 11643588 11691702 11715462 11763873 12702096 12754584 12780504 12833316 12859396 12912534 13045131 14028432 14172488 14231052 14289858 14318898 14348907 14378067 15524784 15588936 15620616 15685164 15781986 15944049 17111088 17216712 17393508 17465382 17537553 17573193 18974736 19053144 19091864 19131876 19170756 19249974 19289094 19368801 20913552 21042648 21258732 21346578 21434787 21478347 23191344 23287176 23383404 23430924 23527746 23672979 25509168 25561008 25666632 25718792 25825068 26090262 26198073 26251313 28344976 28462104 28579716 28637796 28697814 28756134 28874961 28933641 31177872 31241232 31370328 31563972 31888098 32019867 34433424 34787016 34930764 35075106 35146386 35291619 35363339 38106288 38183728 38263752 38341512 38499948 38578188 38737602 39135393 42085296 42517464 42693156 42869574 42956694 43046721 43134201 46574352 46766808 46861848 47055492 47345958 47832147 51333264 51437584 51650136 52180524 52396146 52502626 52612659 52719579 56924208 57159432 57275592 57395628 57512268 57749922 57867282 58106403 62740656 63127944 63776196 64039734 64304361 64435041 69574032 69861528 70150212 70292772 70583238 70726678 71018937 76527504 76683024 76999896 77156376 77475204 78270786 78594219 78753939 85034928 85386312 85739148 85913388 86093442 86268402 86624883 86800923 93533616 93723696 94110984 94691916 95664294 96059601 103300272 104361048 104792292 105005252 105225318 105439158 105874857 106090017 114318864 114551184 114791256 115024536 115499844 115734564 116212806 117406179 126255888 127552392 128079468 128608722 128870082 129402603 139723056 140300424 140585544 141166476 141453356 142037874 143496441 153999792 154312752 154950408 156541572 157188438 157507878 157837977 158158737 170772624 171478296 171826776 172186884 172536804 173249766 173601846 174319209 188221968 189383832 191328588 192119202 192913083 193305123 208722096 209584584 210010504 210450636 210878316 211749714 212180034 213056811 229582512 230049072 230999688 231469128 232425612 234812358 235782657 236261817 255104784 256158936 257217444 257740164 258805206 259874649 260402769 280600848 281171088 282332952 282906712 284075748 286992882 288178803 288764443 309900816 313083144 314376876 315015756 315675954 316317474 317624571 318270051 342956592 343653552 344373768 345073608 346499532 347203692 348638418 352218537 378767664 382657176 384238404 385826166 386610246 388207809 388996729 419169168 420021008 420901272 421756632 423499428 424360068 426113622 430489323 461999376 462938256 464851224 469624716 471565314 472523634 473513931 474476211 512317872 514434888 515480328 517610412 519749298 520805538 522957627 564665904 565813424 568151496 573985764 576357606 577528886 578739249 579915369 626166288 628753752 630031512 631351908 632634948 635249142 636540102 639170433 688747536 690147216 692999064 694407384 697276836 704437074 707347971 708785451 765314352 768476808 771652332 773220492 776415618 777993458 779623947 781208307 841802544 843513264 846998856 848720136 852227244 860978646 864536409 866293329 929702448 939249432 943130628 945047268 947027862 948952422 952873713 954810153 1028869776 1030960656 1035220824 1039498596 1041611076 1045915254 1056655611 1136302992 1147971528 1152715212 1155057772 1157478498 1159830738 1164623427 1166990187 1257507504 1260063024 1262703816 1265269896 1270498284 1273080204 1278340866 1291467969 1385998128 1388814768 1394553672 1408874148 1414695942 1417570902 1423428633 1536953616 1543304664 1546440984 1552831236 1555986916 1559247894 1562416614 1568872881 1693997712 1697440272 1704454488 1721957292 1729072818 1732586658 1736217747 1739746107 1878498864 1886261256 1890094536 1894055724 1897904844 1905747426 1909620306 1917511299 2070441648 2078997192 2083222152 2091830508 2113311222 2122043913 2126356353 2295943056 2305430424 2310115544 2314956996 2319661476 2329246854 2333980374 2338871841 2343624921 2525407632 2530539792 2540996568 2546160408 2556681732 2582935938 2593609227 2598879987 2789107344 2817748296 2829391884 2835141804 2846857266 2858621139 2864430459 3086609328 3092881968 3105662472 3111973832 3118495788 3124833228 3137745762 3169966833 3408908976 3443914584 3458145636 3465173316 3472435494 3479492214 3493870281 3500970561 3772522512 3780189072 3788111448 3795809688 3811494852 3819240612 3835022598 3874403907 4157994384 4166444304 4183661016 4226622444 4244087826 4252712706 4270285899 4278964019 4610860848 4620231088 4629913992 4639322952 4658493708 4667960748 4677743682 4687249842 4706618643 5081993136 5092320816 5113363464 5165871876 5187218454 5197759974 5208653241 5219238321 5635496592 5658783768 5670283608 5693714532 5717242278 5728860918 5752533897 6211324944 6223947664 6236991576 6249666456 6275491524 6339933666 6366131739 6379069059 6887829168 6916291272 6930346632 6944870988 6958984428 6987740562 7001941122 7016615523 7030874763 7576222896 7591619376 7622989704 7638481224 7670045196 7748807814 7780827681 7796639961 8367322032 8453244888 8488175652 8505425412 8540571798 8557928038 8575863417 8593291377 9259827984 9278645904 9316987416 9335921496 9355487364 9374499684 9413237286 9509900499 10226726928 10331743752 10374436908 10395519948 10417306482 10438476642 10481610843 10502911683 11317567536 11340567216 11387429064 11434484556 11457721836 11505067794 11623211721 12473983152 12499332912 12550983048 12679867332 12732263478 12758138118 12810857697 12836892057 13832582544 13860693264 13889741976 13917968856 13975481124 14003882244 14033231046 14061749526 14119855929 15245979408 15276962448 15340090392 15497615628 15561655362 15593279922 15657714963 16906489776 16976351304 17010850824 17081143596 17115856076 17151726834 17186582754 17257601691 18633974832 18671842992 18710974728 18748999368 18826474572 19019800998 19098395217 19137207177 20663487504 20748873816 20791039896 20834612964 20876953284 20963221686 21005823366 21092624289 22774858128 22868969112 22915443672 23010135588 23246423442 23342483043 23389919883 25101966096 25359734664 25464526956 25516276236 25621715394 25673784114 25727590251 25779874131 27779483952 27835937712 27950962248 28007764488 28066462092 28123499052 28239711858 28529701497 30680180784 30995231256 31123310724 31186559844 31315429926 31444832529 31508735049 33952702608 34021701648 34162287192 34231712152 34303453668 34373165508 34515203382 34869635163 37421949456 37497998736 37652949144 38039601996 38196790434 38274414354 38432573091 38510676171 41497747632 41582079792 41669225928 41753906568 41926443372 42011646732 42185248578 42359567787 45737938224 45830887344 46020271176 46492846884 46684966086 46779839766 46973144889 47068604209 50719469328 50929053912 51032552472 51243430788 51347568228 51455180502 51559748262 51772805073 55901924496 56015528976 56132924184 56246998104 56479423716 57059402994 57295185651 57411621531 61990462512 62246621448 62373119688 62630859852 62889665058 63017470098 63277872867 68324574384 68463424304 68606907336 68746331016 69030406764 69739270326 70027449129 70169759649 75305898288 76079203992 76393580868 76548828708 76865146182 77021352342 77182770753 77339622393 83338451856 83507813136 83852886744 84023293464 84370497156 84719135574 85589104491 92040542352 92985693768 93369932172 93559679532 93946289778 94137208418 94334497587 94526205147 101858107824 102065104944 102486861576 102695136456 102910361004 103119496524 103545610146 104608905489 112265848368 112493996208 112958847432 114118805988 114590371302 114823243062 115297719273 115532028513 124493242896 124746239376 125261719704 125779330116 126034940196 126555745734 127078703361 137213814672 137492662032 138060813528 139478540652 140054898258 140339519298 140919434667 141205812627 152158407984 152787161736 153097657416 153730292364 154042704684 154365541506 154679244786 155318415219 167705773488 168046586928 168740994312 169438271148 171178208982 172234864593 185971387536 186739864344 187119359064 187892579556 188274416836 188668995174 189052410294 189833618601 204973723152 205390272912 205820722008 206238993048 207091220292 209217810978 210082347387 210509278947 225917694864 228237611976 229180742604 229646486124 230595438546 231064057026 232018867179 250523439408 251558660232 252069880392 253111491468 254157406722 256767313473 276121627056 278957081304 280109796516 280679038596 281838869334 282411625254 283003492761 283578615441 305574323472 306195314832 307460584728 308085409368 308731083012 309358489572 310636830438 313826716467 337481988624 338876542296 342356417964 344469729186 345893157819 346596085539 373479728688 374238718128 375785159112 376548833672 377337990348 378104820588 379667237202 381236110083 411641444016 412477986096 414182440584 418435621956 420164694774 421018557894 422758304001 423617437881 456475223952 458361485208 459292972248 461190877092 462128114052 464037734358 465955245657 503117320464 504139760784 506222982936 508314813444 513534626946 516704593779 557914162608 560219593032 561358077192 563677738668 564823250508 566006985522 567157230882 569500855803 614921169456 616170818736 617462166024 618716979144 621273660876 627653432934 630247042161 631527836841 677753084592 684712835928 688939458372 691786315638 693192171078 696056601537 751570318224 753097667344 754675980696 756209641176 759334474404 762472220166 770301940419 828364881168 836871243912 840329389548 842037115788 845516608002 847234875762 849010478283 850735846323 916722970416 918585944496 922381754184 924256228104 928075468716 931910491314 941480149401 1012445965872 1016629626888 1027069253892 1033409187558 1037679473457 1039788256617 1120439186064 1122716154384 1127355477336 1129646501016 1132013971044 1134314461764 1139001711606 1143708330249 1234924332048 1237433958288 1242547321752 1255306865868 1260494084322 1263055673682 1268274912003 1270852313643 1369425671856 1377878916744 1383572631276 1386384342156 1392113203074 1397865736971 1509351961392 1512419282352 1518668948808 1524944440332 1540603880838 1550113781337 1673742487824 1680658779096 1684074231576 1691033216004 1694469751524 1698020956566 1701471692646 1708502567409 1844763508368 1848512456208 1856150937432 1863820982628 1882960298802 1894583510523 2033259253776 2054138507784 2066818375116 2075358946914 2079576513234 2088169804611 2254710954672 2259293002032 2264027942088 2268628923528 2278003423212 2287416660498 2310905821257 2485094643504 2510613731736 2520988168644 2526111347364 2536549824006 2541704627286 2552207538969 2755757833488 2767145262552 2772768684312 2784226406148 2795731473942 2824440448203 3037337897616 3049888880664 3081207761676 3100227562674 3113038420371 3119364769851 3361317558192 3368148463152 3382066432008 3388939503048 3396041913132 3402943385292 3417005134818 3712301874864 3727641965256 3765920597604 3789167021046 3804824736009 3812556940929 4108277015568 4133636750232 4150717893828 4159153026468 4176339609222 4193597210913 4528055884176 4537257847056 4556006846424 4574833320996 4621811642514 4650341344011 5021227463472 5041976337288 5052222694728 5073099648012 5083409254572 5104415077938 5125507702227 5534290525104 5545537368624 5568452812296 5591462947884 5648880896406 5683750531569 6099777761328 6162415523352 6200455125348 6226076840742 6238729539702 6264509413833 6764132864016 6777879006096 6792083826264 6805886770584 6834010269636 6932717463771 7455283930512 7531841195208 7578334042092 7609649472018 7625113881858 7656622616907 8267273500464 8301435787656 8318306052936 8352679218444 8387194421826 8473321344609 9112013692848 9149666641992 9243623285028 9300682688022 9339115261113 9358094309553 10083952674576 10104445389456 10146199296024 10166818509144 10208830155876 10251015404454 11136905624592 11182925895768 11297761792812 11367501063138 11414474208027 11437670822787 12324831046704 12400910250696 12452153681484 12477459079404 12529018827666 12580791632739 13584167652528 13611773541168 13668020539272 13865434927542 13951024032033 15063682390416 15156668084184 15219298944036 15250227763716 15313245233814 15376523106681 16602871575312 16636612105872 16705358436888 16774388843652 16946642689218 17051251594707 18299333283984 18487246570056 18601365376044 18678230522226 18716188619106 18793528241499 20292398592048 20333637018288 20417660311752 20502030808908 22365851791536 22595523585624 22735002126276 22828948416054 22875341645574 22969867850721 24801820501392 24904307362968 24954918158808 25058037655332 25161583265478 25419964033827 27336041078544 27730869855084 27902048064066 28074282928659 30313336168368 30438597888072 30500455527432 30626490467628 30753046213362 33410716873776 33548777687304 33893285378436 34102503189414 34243422624081 34313012468361 36974493140112 37202730752088 37356461044452 37432377238212 37587056482998 40835320623504 41004061617816 41853072096099 45191047171248 45470004252552 45657896832108 45750683291148 45939735701442 46129569320043 49808614725936 49909836317616 50116075310664 50323166530956 50839928067654 51153754784121 55461739710168 55804096128132 56148565857318 56380584724497 60877195776144 61000911054864 61252980935256 61506092426724 67097555374608 67786570756872 68205006378828 68486845248162 68626024936722 68909603552163 74405461504176 74712922088904 74864754476424 75174112965996 76259892101481 82008123235632 83706144192198 84222848785977 90940008505104 91315793664216 91501366582296 91879471402884 92259138640086 100232150621328 100646333061912 101679856135308 102307509568242 102730267872243 102939037405083 110923479420336 111608192256264 112297131714636 112761169448994 122505961870512 123012184853448 125559216288297 135573141513744 136410012757656 136973690496324 137252049873444 137819207104326 138388707960129 149425844177808 149729508952848 150348225931992 152519784202962 153461264352363 167412288384396 168445697571954 169141754173491 182631587328432 183002733164592 183758942805768 184518277280172 201292666123824 203359712270616 204615019136484 205460535744486 205878074810166 206728810656489 223216384512528 224594263429272 225522338897988 246024369706896 251118432576594 252668546357931 272820025515312 273947380992648 274504099746888 275638414208652 276777415920258 300696451863984 305039568405924 306922528704726 308817112215249 334824576768792 336891395143908 338283508346982 367517885611536 369036554560344 376677648864891 406719424541232 409230038272968 410921071488972 411756149620332 413457621312978 449188526858544 451044677795976 460383793057089 502236865153188 505337092715862 507425262520473 547894761985296 549008199493776 551276828417304 553554831840516 610079136811848 613845057409452 617634224430498 620186431969467 669649153537584 673782790287816 676567016693964 738073109120688 753355297729782 758005639073793 818460076545936 821842142977944 823512299240664 826915242625956 902089355591952 920767586114178 926451336645747 1004473730306376 1010674185431724 1014850525040946 1102553656834608 1107109663681032 1130032946594673 1220158273623696 1227690114818904 1235268448860996 1240372863938934 1347565580575632 1353134033387928 1381151379171267 1506710595459564 1516011278147586 1522275787561419 1643684285955888 1647024598481328 1653830485251912 1841535172228356 1852902673291494 1860559295908401 2008947460612752 2021348370863448 2029701050081892 2214219327362064 2260065893189346 2274016917221379 2455380229637808 2470536897721992 2480745727877868 2706268066775856 2762302758342534 2779354009937241 3013421190919128 3032022556295172 3044551575122838 3307660970503824 3683070344456712 3705805346582988 3721118591816802 4042696741726896 4059402100163784 4143454137513801 4520131786378692 4548033834442758 4941073795443984 4961491455755736 5524605516685068 5558708019874482 5581677887725203 6026842381838256 6064045112590344 6089103150245676 6822050751664137 7366140688913424 7411610693165976 7442237183633604 8118804200327568 8286908275027602 8338062029811723 9040263572757384 9096067668885516 9922982911511472 11049211033370136 11117416039748964 11163355775450406 12128090225180688 12178206300491352 12430362412541403 13644101503328274 14823221386331952 14884474367267208 16573816550055204 16676124059623446 16745033663175609 18080527145514768 18192135337771032 20466152254992411 22098422066740272 22234832079497928 22326711550900812 24356412600982704 24860724825082806 25014186089435169 27288203006656548 29768948734534416 33147633100110408 33352248119246892 33490067326351218 36384270675542064 40932304509984822 44469664158995856 44653423101801624 49721449650165612 50028372178870338 54576406013313096 61398456764977233 66295266200220816 66704496238493784 66980134652702436 75042558268305507 81864609019969644 89306846203603248 99442899300331224 100056744357740676 109152812026626192 122796913529954466 133408992476987568 133960269305404872 150085116536611014 163729218039939288 184195370294931699 198885798600662448 200113488715481352 225127674804916521 245593827059908932 267920538610809744 300170233073222028 327458436079878576 368390740589863398 400226977430962704 450255349609833042 491187654119817864 600340466146444056 675383024414749563 736781481179726796 900510699219666084 982375308239635728 1200680932292888112 1350766048829499126 1473562962359453592 1801021398439332168 2026149073244248689 2701532097658998252 2947125924718907184 3602042796878664336 4052298146488497378 5403064195317996504 8104596292976994756 10806128390635993008 16209192585953989512 32418385171907979024
- Sum of all divisors σ(n): 104277232668781339671
- Sum of proper divisors (its aliquot sum) s(n): 71858847496873360647
- 32418385171907979024 is an abundant number, because the sum of its proper divisors (71858847496873360647) is greater than itself. Its abundance is 39440462324965381623
Bases of 32418385171907979024
- Binary: 111000001111001010011110110001101110010110101110110100111000100002
- Hexadecimal: 0x1C1E53D8DCB5DA710
- Base-36: 6UASEG6I52900
Squares and roots of 32418385171907979024
- 32418385171907979024 squared (324183851719079790242) is 1050951697154183126696265732116023992576
- 32418385171907979024 cubed (324183851719079790243) is 34070156915414695271361834004000514356297365410035739725824
-
32418385171907979024 is a
perfect square number . Itssquare root is 5693714532 -
The
cube root of 32418385171907979024 is 3188578.5923079059
Scales and comparisons
How big is 32418385171907979024?- 32,418,385,171,907,979,024 seconds is equal to 293,274,701,009 years, 3 weeks, 3 days, 15 hours, 30 minutes, 7 seconds.
-
To count from 1 to 32,418,385,171,907,979,024 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 32418385171907979024 cubic inches would be around 265714.9 feet tall.
Recreational maths with 32418385171907979024
- 32418385171907979024 backwards is 42097970917158381423
- The number of decimal digits it has is: 20
- The sum of 32418385171907979024's digits is 90
- 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 32418385171907979024 - Facts about the integer". Numbermatics.com. 2024. Web. 28 May 2024.
APA style:
Numbermatics. (2024). Number 32418385171907979024 - Facts about the integer. Retrieved 28 May 2024, from https://numbermatics.com/n/32418385171907979024/
Chicago style:
Numbermatics. 2024. "Number 32418385171907979024 - Facts about the integer". https://numbermatics.com/n/32418385171907979024/
The information we have on file for 32418385171907979024 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 32418385171907979024, math, Factors of 32418385171907979024, curriculum, school, college, exams, university, Prime factorization of 32418385171907979024, STEM, science, technology, engineering, physics, economics, calculator, thirty-two quintillion, four hundred eighteen quadrillion, three hundred eighty-five trillion, one hundred seventy-one billion, nine hundred seven million, nine hundred seventy-nine thousand and twenty-four.