32225193197568
32,225,193,197,568 is an even composite number composed of five prime numbers multiplied together.
32225193197568 is an even composite number. It is composed of five distinct prime numbers multiplied together. It has a total of two thousand, three hundred four divisors.
Prime factorization of 32225193197568:
215 × 38 × 73 × 19 × 23
(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 7 × 7 × 7 × 19 × 23)See below for interesting mathematical facts about the number 32225193197568 from the Numbermatics database.
Names of 32225193197568
- Cardinal: 32225193197568 can be written as Thirty-two trillion, two hundred twenty-five billion, one hundred ninety-three million, one hundred ninety-seven thousand, five hundred sixty-eight.
Scientific notation
- Scientific notation: 3.2225193197568 × 1013
Factors of 32225193197568
Divisors of 32225193197568
- Number of divisors d(n): 2304
-
Complete list of divisors:
1 2 3 4 6 7 8 9 12 14 16 18 19 21 23 24 27 28 32 36 38 42 46 48 49 54 56 57 63 64 69 72 76 81 84 92 96 98 108 112 114 126 128 133 138 144 147 152 161 162 168 171 184 189 192 196 207 216 224 228 243 252 256 266 276 288 294 304 322 324 336 342 343 368 378 384 392 399 414 432 437 441 448 456 483 486 504 512 513 532 552 567 576 588 608 621 644 648 672 684 686 729 736 756 768 784 798 828 864 874 882 896 912 931 966 972 1008 1024 1026 1029 1064 1104 1127 1134 1152 1176 1197 1216 1242 1288 1296 1311 1323 1344 1368 1372 1449 1458 1472 1512 1536 1539 1568 1596 1656 1701 1728 1748 1764 1792 1824 1862 1863 1932 1944 2016 2048 2052 2058 2128 2187 2208 2254 2268 2304 2352 2394 2432 2484 2576 2592 2622 2646 2688 2736 2744 2793 2898 2916 2944 3024 3059 3072 3078 3087 3136 3192 3312 3381 3402 3456 3496 3528 3584 3591 3648 3724 3726 3864 3888 3933 3969 4032 4096 4104 4116 4256 4347 4374 4416 4508 4536 4608 4617 4704 4788 4864 4968 5103 5152 5184 5244 5292 5376 5472 5488 5586 5589 5796 5832 5888 6048 6118 6144 6156 6174 6272 6384 6517 6561 6624 6762 6804 6912 6992 7056 7168 7182 7296 7448 7452 7728 7776 7866 7889 7938 8064 8192 8208 8232 8379 8512 8694 8748 8832 9016 9072 9177 9216 9234 9261 9408 9576 9728 9936 10143 10206 10304 10368 10488 10584 10752 10773 10944 10976 11172 11178 11592 11664 11776 11799 11907 12096 12236 12288 12312 12348 12544 12768 13034 13041 13122 13248 13524 13608 13824 13851 13984 14112 14336 14364 14592 14896 14904 15309 15456 15552 15732 15778 15876 16128 16384 16416 16464 16758 16767 17024 17388 17496 17664 18032 18144 18354 18432 18468 18522 18816 19152 19456 19551 19872 20286 20412 20608 20736 20976 21168 21413 21504 21546 21888 21952 22344 22356 23184 23328 23552 23598 23667 23814 24192 24472 24576 24624 24696 25088 25137 25536 26068 26082 26244 26496 27048 27216 27531 27648 27702 27783 27968 28224 28672 28728 29184 29792 29808 30429 30618 30912 31104 31464 31556 31752 32256 32319 32768 32832 32928 33516 33534 34048 34776 34992 35328 35397 35721 36064 36288 36708 36864 36936 37044 37632 38304 38912 39102 39123 39744 40572 40824 41216 41472 41553 41952 42336 42826 43008 43092 43776 43904 44688 44712 45927 46368 46656 47104 47196 47334 47628 48384 48944 49152 49248 49392 50176 50274 50301 51072 52136 52164 52488 52992 54096 54432 55062 55296 55404 55566 55936 56448 57344 57456 58368 58653 59584 59616 60858 61236 61824 62208 62928 63112 63504 64239 64512 64638 65664 65856 67032 67068 68096 69552 69984 70656 70794 71001 71442 72128 72576 73416 73728 73872 74088 75264 75411 76608 77824 78204 78246 79488 81144 81648 82432 82593 82944 83106 83349 83904 84672 85652 86016 86184 87552 87808 89376 89424 91287 91854 92736 93312 94208 94392 94668 95256 96768 96957 97888 98304 98496 98784 100352 100548 100602 102144 104272 104328 104976 105984 106191 107163 108192 108864 110124 110592 110808 111132 111872 112896 114688 114912 116736 117306 117369 119168 119232 121716 122472 123648 124416 124659 125856 126224 127008 128478 129024 129276 131328 131712 134064 134136 136192 139104 139968 141312 141588 142002 142884 144256 145152 146832 147456 147744 148176 149891 150528 150822 150903 153216 155648 156408 156492 158976 162288 163296 164864 165186 165888 166212 166698 167808 169344 171304 172032 172368 175104 175616 175959 178752 178848 182574 183708 185472 186624 188416 188784 189336 190512 192717 193536 193914 195776 196992 197568 200704 201096 201204 204288 208544 208656 209952 211968 212382 213003 214326 216384 217728 220248 221184 221616 222264 223744 225792 226233 229376 229824 233472 234612 234738 238336 238464 243432 244944 247296 247779 248832 249318 250047 251712 252448 254016 256956 258048 258552 262656 263424 268128 268272 272384 273861 278208 279936 282624 283176 284004 285768 288512 290304 290871 293664 294912 295488 296352 299782 301056 301644 301806 306432 311296 312816 312984 317952 318573 321489 324576 326592 329728 330372 331776 332424 333396 335616 338688 342608 344064 344736 350208 351232 351918 352107 357504 357696 365148 367416 370944 373248 376832 377568 378672 381024 385434 387072 387828 391552 393984 395136 401408 402192 402408 408576 417088 417312 419904 423936 424764 426006 428652 432768 435456 440496 442368 443232 444528 447488 449673 451584 452466 459648 466944 469224 469476 476672 476928 486864 489888 494592 495558 497664 498636 500094 503424 504896 508032 513912 516096 517104 525312 526848 527877 536256 536544 544768 547722 556416 559872 565248 566352 568008 571536 577024 578151 580608 581742 587328 590976 592704 599564 602112 603288 603612 612864 622592 625632 625968 635904 637146 639009 642978 649152 653184 659456 660744 663552 664848 666792 671232 677376 678699 685216 688128 689472 700416 702464 703836 704214 715008 715392 730296 734832 741888 743337 746496 750141 753664 755136 757344 762048 770868 774144 775656 783104 787968 790272 802816 804384 804816 817152 821583 834176 834624 839808 847872 849528 852012 857304 865536 870912 872613 880992 884736 886464 889056 894976 899346 903168 904932 919296 933888 938448 938952 953344 953856 955719 973728 979776 989184 991116 995328 997272 1000188 1006848 1009792 1016064 1027824 1032192 1034208 1050624 1053696 1055754 1056321 1072512 1073088 1089536 1095444 1112832 1119744 1130496 1132704 1136016 1143072 1154048 1156302 1161216 1163484 1174656 1181952 1185408 1199128 1204224 1206576 1207224 1225728 1251264 1251936 1271808 1274292 1278018 1285956 1298304 1306368 1318912 1321488 1327104 1329696 1333584 1342464 1349019 1354752 1357398 1370432 1378944 1400832 1404928 1407672 1408428 1430016 1430784 1460592 1469664 1483776 1486674 1492992 1500282 1510272 1514688 1524096 1541736 1548288 1551312 1566208 1575936 1580544 1583631 1605632 1608768 1609632 1634304 1643166 1668352 1669248 1679616 1695744 1699056 1704024 1714608 1731072 1734453 1741824 1745226 1761984 1772928 1778112 1789952 1798692 1806336 1809864 1838592 1867776 1876896 1877904 1906688 1907712 1911438 1917027 1947456 1959552 1978368 1982232 1990656 1994544 2000376 2013696 2019584 2032128 2036097 2055648 2064384 2068416 2101248 2107392 2111508 2112642 2145024 2146176 2179072 2190888 2225664 2230011 2239488 2250423 2260992 2265408 2272032 2286144 2308096 2312604 2322432 2326968 2349312 2363904 2370816 2398256 2408448 2413152 2414448 2451456 2464749 2502528 2503872 2543616 2548584 2556036 2571912 2596608 2612736 2637824 2642976 2654208 2659392 2667168 2684928 2698038 2709504 2714796 2740864 2757888 2801664 2809856 2815344 2816856 2860032 2861568 2867157 2921184 2939328 2967552 2973348 2985984 3000564 3020544 3029376 3048192 3083472 3096576 3102624 3132416 3151872 3161088 3167262 3217536 3219264 3268608 3286332 3336704 3338496 3359232 3391488 3398112 3408048 3429216 3462144 3468906 3483648 3490452 3523968 3545856 3556224 3579904 3597384 3612672 3619728 3677184 3753792 3755808 3813376 3815424 3822876 3834054 3894912 3919104 3956736 3964464 3981312 3989088 4000752 4027392 4039168 4047057 4064256 4072194 4111296 4136832 4202496 4214784 4223016 4225284 4290048 4292352 4358144 4381776 4451328 4460022 4478976 4500846 4530816 4544064 4572288 4616192 4625208 4644864 4653936 4698624 4727808 4741632 4750893 4796512 4816896 4826304 4828896 4902912 4929498 5005056 5007744 5087232 5097168 5112072 5143824 5193216 5203359 5225472 5275648 5285952 5318784 5334336 5369856 5396076 5419008 5429592 5481728 5515776 5603328 5619712 5630688 5633712 5720064 5723136 5734314 5751081 5842368 5878656 5935104 5946696 5971968 6001128 6041088 6058752 6096384 6108291 6166944 6193152 6205248 6264832 6303744 6322176 6334524 6435072 6438528 6537216 6572664 6673408 6676992 6690033 6718464 6782976 6796224 6816096 6858432 6924288 6937812 6967296 6980904 7047936 7091712 7112448 7159808 7194768 7225344 7239456 7354368 7394247 7507584 7511616 7626752 7630848 7645752 7668108 7789824 7838208 7913472 7928928 7962624 7978176 8001504 8054784 8078336 8094114 8128512 8144388 8222592 8273664 8404992 8429568 8446032 8450568 8580096 8584704 8763552 8902656 8920044 8957952 9001692 9061632 9088128 9144576 9232384 9250416 9289728 9307872 9397248 9455616 9483264 9501786 9593024 9652608 9657792 9805824 9858996 10010112 10015488 10174464 10194336 10224144 10287648 10386432 10406718 10450944 10571904 10637568 10668672 10739712 10792152 10838016 10859184 10963456 11031552 11239424 11261376 11267424 11440128 11446272 11468628 11502162 11684736 11757312 11870208 11893392 11943936 12002256 12082176 12117504 12141171 12192768 12216582 12333888 12410496 12529664 12607488 12644352 12669048 12870144 12877056 13074432 13145328 13346816 13353984 13380066 13436928 13592448 13632192 13716864 13848576 13875624 13934592 13961808 14095872 14183424 14224896 14252679 14319616 14389536 14450688 14478912 14708736 14788494 15015168 15023232 15253504 15261696 15291504 15336216 15579648 15610077 15676416 15826944 15857856 15956352 16003008 16109568 16156672 16188228 16257024 16288776 16445184 16547328 16809984 16859136 16892064 16901136 17160192 17169408 17253243 17527104 17805312 17840088 17915904 18003384 18123264 18176256 18289152 18464768 18500832 18579456 18615744 18794496 18911232 18966528 19003572 19186048 19305216 19315584 19611648 19717992 20020224 20030976 20070099 20348928 20388672 20448288 20575296 20772864 20813436 20901888 21143808 21275136 21337344 21479424 21584304 21676032 21718368 21926912 22063104 22522752 22534848 22880256 22892544 22937256 23004324 23369472 23514624 23740416 23786784 23887872 24004512 24164352 24235008 24282342 24385536 24433164 24667776 24820992 25059328 25214976 25288704 25338096 25740288 25754112 26290656 26693632 26707968 26760132 26873856 27184896 27264384 27433728 27697152 27751248 27869184 27923616 28191744 28366848 28449792 28505358 28779072 28957824 29417472 29576988 30030336 30046464 30507008 30523392 30583008 30672432 31159296 31220154 31352832 31715712 31912704 32006016 32219136 32313344 32376456 32514048 32577552 32890368 33094656 33718272 33784128 33802272 34320384 34338816 34506486 35054208 35610624 35680176 35831808 36006768 36246528 36352512 36423513 36578304 36929536 37001664 37231488 37588992 37822464 37933056 38007144 38372096 38610432 38631168 39223296 39435984 40040448 40061952 40140198 40777344 40896576 41150592 41545728 41626872 41803776 42287616 42550272 42674688 42758037 42958848 43168608 43352064 43436736 43853824 44126208 45045504 45069696 45760512 45785088 45874512 46008648 46738944 46830231 47029248 47480832 47573568 48009024 48328704 48470016 48564684 48771072 48866328 49335552 49641984 50118656 50429952 50577408 50676192 51480576 51508224 51759729 52581312 53387264 53415936 53520264 53747712 54369792 54528768 54867456 55394304 55502496 55738368 55847232 56383488 56733696 56899584 57010716 57558144 57915648 58834944 59153976 60060672 60092928 61046784 61166016 61344864 62318592 62440308 62705664 63431424 63825408 64012032 64438272 64626688 64752912 65028096 65155104 65780736 66189312 67568256 67604544 68640768 68677632 69012972 70108416 71221248 71360352 71663616 72013536 72493056 72705024 72847026 73156608 74003328 74462976 75177984 75644928 75866112 76014288 76744192 77220864 77262336 78871968 80080896 80123904 80280396 81554688 81793152 82301184 83091456 83253744 83607552 84575232 85100544 85349376 85516074 86337216 86873472 87707648 88252416 90091008 90139392 91521024 91570176 91749024 92017296 93477888 93660462 94058496 95147136 96018048 96657408 96940032 97129368 97542144 97732656 98671104 99283968 100237312 101154816 101352384 102961152 103016448 103519458 105162624 106774528 106831872 107040528 107495424 108739584 109057536 109270539 109734912 110788608 111004992 111694464 112766976 113467392 113799168 114021432 115116288 115831296 117669888 118307952 120121344 120185856 122332032 122689728 124637184 124880616 125411328 126862848 127650816 128024064 128876544 129253376 129505824 130056192 130310208 131561472 132378624 135136512 135209088 137281536 137355264 138025944 140216832 140490693 142442496 142720704 144027072 144986112 145410048 145694052 146313216 148006656 148925952 150355968 151289856 151732224 152028576 153488384 154441728 154524672 157743936 160161792 160247808 160560792 163109376 163586304 164602368 166182912 166507488 167215104 169150464 170201088 170698752 171032148 172674432 173746944 175415296 176504832 180182016 180278784 183140352 183498048 184034592 186955776 187320924 188116992 190294272 192036096 193314816 193880064 194258736 195084288 195465312 197342208 198567936 202704768 205922304 206032896 207038916 210325248 213549056 213663744 214081056 214990848 217479168 218115072 218541078 219469824 222009984 223388928 225533952 226934784 227598336 228042864 230232576 231662592 236615904 240242688 240371712 244664064 245379456 249274368 249761232 250822656 253725696 255301632 256048128 258506752 259011648 260620416 263122944 264757248 270273024 270418176 274563072 274710528 276051888 280433664 280981386 285441408 288054144 289972224 290820096 291388104 292626432 296013312 297851904 300711936 303464448 304057152 306976768 308883456 309049344 315487872 320323584 320495616 321121584 326218752 327172608 327811617 329204736 332365824 333014976 338300928 340402176 341397504 342064296 345348864 347493888 350830592 353009664 360364032 360557568 366996096 368069184 373911552 374641848 376233984 380588544 384072192 386629632 387760128 388517472 390168576 390930624 394684416 397135872 405409536 411844608 412065792 414077832 420650496 427327488 428162112 434958336 436230144 437082156 438939648 444019968 446777856 451067904 453869568 455196672 456085728 460465152 463325184 473231808 480485376 480743424 489328128 490758912 498548736 499522464 501645312 507451392 510603264 512096256 518023296 521240832 526245888 529514496 540546048 540836352 549421056 552103776 560867328 561962772 570882816 576108288 579944448 581640192 582776208 585252864 592026624 595703808 608114304 613953536 617766912 618098688 630975744 640647168 640991232 642243168 652437504 654345216 655623234 658409472 666029952 676601856 680804352 682795008 684128592 690697728 694987776 701661184 720728064 721115136 733992192 736138368 747823104 749283696 752467968 761177088 768144384 775520256 777034944 781861248 789368832 794271744 810819072 823689216 824131584 828155664 841300992 856324224 869916672 872460288 874164312 877879296 888039936 893555712 902135808 910393344 912171456 920930304 926650368 946463616 960970752 961486848 978656256 981517824 983434851 997097472 999044928 1014902784 1021206528 1024192512 1036046592 1042481664 1052491776 1059028992 1081092096 1081672704 1104207552 1121734656 1123925544 1141765632 1152216576 1159888896 1163280384 1165552416 1170505728 1184053248 1191407616 1216228608 1227907072 1235533824 1236197376 1261951488 1281982464 1284486336 1304875008 1308690432 1311246468 1316818944 1332059904 1353203712 1361608704 1365590016 1368257184 1381395456 1389975552 1441456128 1442230272 1467984384 1472276736 1495646208 1498567392 1504935936 1522354176 1536288768 1554069888 1563722496 1578737664 1588543488 1621638144 1648263168 1656311328 1682601984 1712648448 1739833344 1744920576 1748328624 1755758592 1776079872 1787111424 1824342912 1841860608 1853300736 1892927232 1921941504 1922973696 1957312512 1963035648 1966869702 1998089856 2029805568 2042413056 2048385024 2072093184 2084963328 2104983552 2162184192 2163345408 2208415104 2243469312 2247851088 2283531264 2304433152 2326560768 2331104832 2368106496 2382815232 2432457216 2455814144 2471067648 2472394752 2523902976 2568972672 2609750016 2617380864 2622492936 2633637888 2664119808 2706407424 2731180032 2736514368 2762790912 2779951104 2882912256 2884460544 2935968768 2944553472 2991292416 2997134784 3044708352 3072577536 3108139776 3127444992 3157475328 3177086976 3243276288 3312622656 3365203968 3425296896 3479666688 3489841152 3496657248 3511517184 3552159744 3574222848 3648685824 3683721216 3706601472 3785854464 3845947392 3914625024 3926071296 3933739404 3996179712 4059611136 4084826112 4096770048 4144186368 4169926656 4324368384 4326690816 4416830208 4486938624 4495702176 4567062528 4608866304 4662209664 4736212992 4765630464 4864914432 4911628288 4944789504 5047805952 5137945344 5219500032 5234761728 5244985872 5267275776 5328239616 5473028736 5525581824 5559902208 5765824512 5768921088 5871937536 5889106944 5994269568 6089416704 6145155072 6216279552 6254889984 6314950656 6486552576 6625245312 6730407936 6850593792 6979682304 6993314496 7104319488 7148445696 7297371648 7367442432 7413202944 7571708928 7829250048 7852142592 7867478808 7992359424 8119222272 8193540096 8288372736 8339853312 8648736768 8653381632 8833660416 8973877248 8991404352 9134125056 9217732608 9324419328 9472425984 9531260928 9729828864 10095611904 10275890688 10439000064 10469523456 10489971744 10534551552 10656479232 10946057472 11051163648 11119804416 11537842176 11743875072 11778213888 11988539136 12178833408 12290310144 12432559104 12509779968 12973105152 13250490624 13460815872 13701187584 13986628992 14208638976 14296891392 14594743296 14734884864 15143417856 15658500096 15704285184 15734957616 15984718848 16576745472 16679706624 17297473536 17306763264 17667320832 17982808704 18268250112 18435465216 18648838656 18944851968 19459657728 20191223808 20551781376 20939046912 20979943488 21312958464 21892114944 22102327296 22239608832 23487750144 23556427776 23977078272 24357666816 24580620288 24865118208 25019559936 25946210304 26500981248 26921631744 27402375168 27973257984 28417277952 28593782784 29189486592 30286835712 31317000192 31408570368 31469915232 31969437696 33153490944 33359413248 34613526528 35334641664 35965617408 36536500224 36870930432 37297677312 38919315456 40382447616 41103562752 41959886976 42625916928 43784229888 44204654592 46975500288 47112855552 47954156544 49730236416 50039119872 51892420608 53001962496 54804750336 55946515968 56834555904 58378973184 60573671424 62817140736 62939830464 63938875392 66306981888 66718826496 70669283328 71931234816 73073000448 73741860864 74595354624 77838630912 80764895232 82207125504 83919773952 85251833856 87568459776 93951000576 94225711104 95908313088 99460472832 100078239744 106003924992 109609500672 111893031936 116757946368 121147342848 125879660928 127877750784 132613963776 141338566656 143862469632 149190709248 155677261824 164414251008 167839547904 170503667712 175136919552 188451422208 191816626176 198920945664 200156479488 212007849984 219219001344 223786063872 233515892736 242294685696 251759321856 255755501568 282677133312 287724939264 298381418496 328828502016 335679095808 350273839104 383633252352 397841891328 424015699968 447572127744 467031785472 503518643712 511511003136 565354266624 575449878528 596762836992 657657004032 671358191616 700547678208 767266504704 848031399936 895144255488 1007037287424 1150899757056 1193525673984 1342716383232 1401095356416 1534533009408 1696062799872 1790288510976 2014074574848 2301799514112 2685432766464 3580577021952 4028149149696 4603599028224 5370865532928 8056298299392 10741731065856 16112596598784 32225193197568
- Sum of all divisors σ(n): 123826547520000
- Sum of proper divisors (its aliquot sum) s(n): 91601354322432
- 32225193197568 is an abundant number, because the sum of its proper divisors (91601354322432) is greater than itself. Its abundance is 59376161124864
Bases of 32225193197568
- Binary: 1110101001111000000110011000110000000000000002
- Hexadecimal: 0x1D4F03318000
- Base-36: BF81S0000
Squares and roots of 32225193197568
- 32225193197568 squared (322251931975682) is 1038463076620582900281114624
- 32225193197568 cubed (322251931975683) is 33464673272639144855833995456261686034432
-
The
square root of 32225193197568 is 5676723.8084627651 -
The
cube root of 32225193197568 is 31822.3203388593
Scales and comparisons
How big is 32225193197568?- 32,225,193,197,568 seconds is equal to 1,024,661 years, 24 weeks, 1 day, 2 hours, 52 minutes, 48 seconds.
-
To count from 1 to 32,225,193,197,568 would take you about two million, five hundred sixty-one thousand, six hundred fifty-three 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 32225193197568 cubic inches would be around 2651.9 feet tall.
Recreational maths with 32225193197568
- 32225193197568 backwards is 86579139152223
- 32225193197568 is a
Harshad number . - The number of decimal digits it has is: 14
- The sum of 32225193197568's digits is 63
- 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 32225193197568 - Facts about the integer". Numbermatics.com. 2024. Web. 15 May 2024.
APA style:
Numbermatics. (2024). Number 32225193197568 - Facts about the integer. Retrieved 15 May 2024, from https://numbermatics.com/n/32225193197568/
Chicago style:
Numbermatics. 2024. "Number 32225193197568 - Facts about the integer". https://numbermatics.com/n/32225193197568/
The information we have on file for 32225193197568 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 32225193197568, math, Factors of 32225193197568, curriculum, school, college, exams, university, Prime factorization of 32225193197568, STEM, science, technology, engineering, physics, economics, calculator, thirty-two trillion, two hundred twenty-five billion, one hundred ninety-three million, one hundred ninety-seven thousand, five hundred sixty-eight.