48409966107360
48,409,966,107,360 is an even composite number composed of eight prime numbers multiplied together.
48409966107360 is an even composite number. It is composed of eight distinct prime numbers multiplied together. It has a total of two thousand, three hundred four divisors.
Prime factorization of 48409966107360:
25 × 35 × 5 × 11 × 13 × 47 × 61 × 3037
(2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 5 × 11 × 13 × 47 × 61 × 3037)See below for interesting mathematical facts about the number 48409966107360 from the Numbermatics database.
Names of 48409966107360
- Cardinal: 48409966107360 can be written as Forty-eight trillion, four hundred nine billion, nine hundred sixty-six million, one hundred seven thousand, three hundred sixty.
Scientific notation
- Scientific notation: 4.840996610736 × 1013
Factors of 48409966107360
Divisors of 48409966107360
- Number of divisors d(n): 2304
-
Complete list of divisors:
1 2 3 4 5 6 8 9 10 11 12 13 15 16 18 20 22 24 26 27 30 32 33 36 39 40 44 45 47 48 52 54 55 60 61 65 66 72 78 80 81 88 90 94 96 99 104 108 110 117 120 122 130 132 135 141 143 144 156 160 162 165 176 180 183 188 195 198 208 216 220 234 235 240 243 244 260 264 270 282 286 288 297 305 312 324 330 351 352 360 366 376 390 396 405 416 423 429 432 440 468 470 480 486 488 495 517 520 528 540 549 564 572 585 594 610 611 624 648 660 671 702 705 715 720 732 752 780 792 793 810 846 858 864 880 891 915 936 940 972 976 990 1034 1040 1053 1056 1080 1098 1128 1144 1170 1188 1215 1220 1222 1248 1269 1287 1296 1320 1342 1404 1410 1430 1440 1464 1485 1504 1551 1560 1584 1586 1620 1647 1692 1716 1755 1760 1782 1830 1833 1872 1880 1944 1952 1980 2013 2068 2080 2106 2115 2145 2160 2196 2256 2288 2340 2376 2379 2430 2440 2444 2538 2574 2585 2592 2640 2673 2684 2745 2808 2820 2860 2867 2928 2970 3037 3055 3102 3120 3159 3168 3172 3240 3294 3355 3384 3432 3510 3564 3660 3666 3744 3760 3807 3861 3888 3960 3965 4026 4136 4212 4230 4290 4320 4392 4455 4512 4576 4653 4680 4752 4758 4860 4880 4888 4941 5076 5148 5170 5265 5280 5346 5368 5490 5499 5616 5640 5720 5734 5856 5940 6039 6074 6110 6204 6240 6318 6344 6345 6435 6480 6588 6710 6721 6768 6864 7020 7128 7137 7320 7332 7520 7614 7722 7755 7776 7920 7930 8052 8235 8272 8424 8460 8580 8601 8723 8784 8910 9111 9165 9306 9360 9504 9516 9720 9760 9776 9882 10065 10152 10296 10340 10530 10692 10736 10980 10998 11232 11280 11421 11440 11468 11583 11880 11895 12078 12148 12220 12408 12636 12688 12690 12870 12960 13176 13365 13420 13442 13536 13728 13959 14040 14256 14274 14335 14640 14664 14823 15185 15228 15444 15510 15795 15840 15860 16104 16470 16497 16544 16848 16920 17160 17202 17446 17568 17820 18117 18222 18330 18612 18720 19032 19035 19305 19440 19552 19764 20130 20163 20304 20592 20680 21060 21384 21411 21472 21960 21996 22560 22842 22880 22936 23166 23265 23760 23790 24156 24296 24440 24705 24816 25272 25376 25380 25740 25803 26169 26352 26730 26840 26884 27333 27495 27918 28080 28512 28548 28670 29280 29328 29646 30195 30370 30456 30888 31020 31537 31590 31720 32208 32940 32994 33407 33605 33696 33840 34320 34404 34749 34892 35640 35685 36234 36444 36660 37224 37271 38064 38070 38610 38880 39481 39528 40260 40326 40608 41184 41360 41877 42120 42768 42822 43005 43615 43920 43992 45555 45684 45872 46332 46530 47520 47580 48312 48592 48880 49410 49491 49632 50544 50760 51480 51606 52338 52704 53460 53680 53768 54351 54666 54990 55836 56160 57096 57105 57340 57915 58656 59292 60390 60489 60740 60912 61776 62040 63074 63180 63440 64233 64416 65880 65988 66814 67210 67680 68640 68808 69498 69784 69795 71280 71370 72468 72888 73320 74115 74448 74542 76128 76140 77220 77409 78507 78962 79056 80520 80652 81999 82485 82720 83754 84240 85536 85644 86010 87230 87840 87984 90585 91110 91368 91744 92664 93060 94611 95160 96624 97184 97760 98820 98982 100221 100815 101088 101520 102960 103212 104676 106920 107055 107360 107536 108702 109332 109980 111672 111813 114192 114210 114680 115830 118443 118584 120780 120978 121480 121824 123552 124080 125631 126148 126360 126880 128466 129015 130845 131760 131976 133628 134420 136665 137616 138996 139568 139590 142560 142739 142740 144936 145776 146640 148230 148473 148896 149084 152280 154440 154818 157014 157685 157924 158112 161040 161304 163053 163998 164970 167035 167508 168480 171288 172020 173745 174460 175968 181170 181467 182220 182736 185257 185328 186120 186355 189222 190320 192699 193248 197405 197640 197964 200442 201630 203040 205920 206424 209352 209385 213840 214110 215072 217404 218664 219960 223344 223626 228384 228420 229360 231660 232227 235521 236886 237168 241560 241956 242960 245997 247455 248160 251262 252296 252720 256932 258030 261690 263520 263952 267256 268840 271755 273330 275232 277992 279136 279180 283833 285478 285480 289872 291552 293280 296460 296946 298168 300663 302445 304560 308880 309636 314028 315370 315848 321165 322080 322608 326106 327996 329940 334070 335016 335439 342576 344040 347490 348920 355329 362340 362934 364440 365472 370514 370656 372240 372710 378444 380640 385398 387045 392535 394810 395280 395928 400884 403260 409981 409995 412848 418704 418770 427680 428217 428220 434291 434808 437328 439920 446688 447252 456840 458720 463320 464454 471042 473055 473772 474336 483120 483912 485920 491994 494910 501105 502524 504592 505440 513864 516060 523380 527904 534512 537680 543510 544401 546660 555771 555984 558360 559065 567666 570956 570960 579744 592215 592920 593892 596336 601326 604890 609120 617760 619272 628056 628155 630740 631696 642330 645216 652212 655992 659880 668140 670032 670878 685152 688080 694980 696681 697840 706563 710658 713695 724680 725868 728880 737991 741028 742365 744480 745420 756888 770796 774090 785070 789620 790560 791856 801768 806520 815265 819962 819990 825696 837408 837540 851499 856434 856440 868582 869616 874656 879840 894504 901989 907335 913680 926285 926640 928908 942084 946110 947544 963495 966240 967824 983988 989820 1002210 1005048 1006317 1009184 1027728 1032120 1046760 1065987 1069024 1075360 1087020 1088802 1093320 1111542 1111968 1116720 1118130 1135332 1141912 1141920 1161135 1177605 1184430 1185840 1187784 1192672 1202652 1209780 1229943 1229985 1238544 1256112 1256310 1261480 1263392 1284651 1284660 1302873 1304424 1311984 1319760 1336280 1340064 1341756 1376160 1389960 1393362 1395680 1413126 1419165 1421316 1427390 1449360 1451736 1457760 1475982 1482056 1484730 1490840 1503315 1513776 1541592 1548180 1570129 1570140 1579240 1583712 1603536 1613040 1630530 1633203 1639924 1639980 1667313 1675080 1677195 1702998 1712868 1712880 1737164 1739232 1776645 1789008 1803978 1814670 1827360 1852570 1853280 1855607 1857816 1884168 1892220 1895088 1926990 1935648 1967976 1979640 2004420 2010096 2012634 2037827 2049905 2055456 2064240 2093520 2119689 2131974 2141085 2171455 2174040 2177604 2186640 2223084 2233440 2236260 2270664 2283824 2322270 2355210 2368860 2371680 2375568 2405304 2408341 2419560 2459886 2459970 2477088 2512224 2512620 2522960 2554497 2569302 2569320 2605746 2608848 2623968 2639520 2672560 2683512 2705967 2722005 2778855 2779920 2786724 2826252 2838330 2842632 2854780 2898720 2903472 2951964 2964112 2969460 2981680 3006630 3018951 3027552 3083184 3096360 3140258 3140280 3158480 3197961 3207072 3226080 3261060 3266406 3279848 3279960 3334626 3350160 3354390 3405996 3425736 3425760 3474328 3483405 3532815 3553290 3578016 3607956 3629340 3689829 3689955 3705140 3711214 3715632 3768336 3784440 3790176 3853953 3853980 3908619 3935952 3959280 4008840 4020192 4025268 4075654 4099810 4128480 4187040 4239378 4257495 4263948 4282170 4342910 4348080 4355208 4373280 4446168 4472520 4509945 4541328 4567648 4644540 4710387 4710420 4737720 4751136 4810608 4816682 4839120 4919772 4919940 5001939 5025240 5031585 5045920 5108994 5138604 5138640 5211492 5217696 5329935 5345120 5367024 5411934 5444010 5557710 5559840 5566821 5573448 5652504 5676660 5685264 5709560 5806944 5903928 5928224 5938920 5963360 6013260 6037902 6113481 6149715 6166368 6192720 6280516 6280560 6316960 6395922 6423255 6514365 6522120 6532812 6559696 6559920 6669252 6700320 6708780 6811992 6851472 6948656 6966810 7065630 7106580 7215912 7225023 7258680 7379658 7379910 7410280 7422428 7431264 7536672 7568880 7663491 7707906 7707960 7817238 7850645 7871904 7918560 8017680 8050536 8117901 8151308 8166015 8199620 8336565 8478756 8514990 8527896 8564340 8685820 8696160 8707079 8710416 8892336 8945040 9019890 9056853 9082656 9278035 9289080 9420774 9420840 9475440 9593883 9621216 9633364 9678240 9839544 9839880 10003878 10050480 10063170 10189135 10217988 10277208 10277280 10422984 10598445 10659870 10734048 10823868 10888020 11069487 11115420 11133642 11146896 11305008 11353320 11370528 11419120 11561859 11725857 11807856 11877840 12026520 12041705 12075804 12226962 12299430 12385440 12561032 12561120 12772485 12791844 12846510 13028730 13044240 13065624 13119392 13119840 13338504 13417560 13529835 13623984 13702944 13897312 13933620 14131161 14131260 14213160 14431824 14450046 14517360 14759316 14759820 14820560 14844856 15005817 15094755 15137760 15326982 15415812 15415920 15634476 15701290 15989805 16035360 16101072 16235802 16302616 16332030 16399240 16673130 16700463 16957512 17029980 17055792 17128680 17371640 17414158 17420832 17784672 17890080 18039780 18113706 18340443 18449145 18556070 18578160 18841548 18841680 18950880 19187766 19266728 19269765 19543095 19679088 19679760 20007756 20100960 20126340 20378270 20411677 20435976 20554416 20845968 21196890 21319740 21647736 21675069 21776040 22138974 22230840 22267284 22293792 22610016 22706640 22838240 23123718 23451714 23551935 23615712 23755680 24053040 24083410 24151608 24453924 24598860 25009695 25122064 25544970 25583688 25693020 26057460 26088480 26121237 26131248 26491751 26677008 26835120 27059670 27247968 27834105 27867240 28262322 28262520 28426320 28863648 28900092 29034720 29518632 29519640 29641120 29689712 30011634 30189510 30567405 30653964 30831624 30831840 31268952 31402580 31979610 32202144 32471604 32605232 32664060 32798480 33208461 33346260 33400926 33915024 34059960 34111584 34257360 34685577 34743280 34828316 35177571 36079560 36125115 36227412 36680886 36898290 37112140 37156320 37683096 37683360 38317455 38375532 38533456 38539530 39086190 39358176 39359520 40015512 40252680 40589505 40756540 40823354 40871952 41108832 41691936 42393483 42393780 42639480 43295472 43350138 43535395 43552080 44277948 44461680 44534568 45017451 45284265 45413280 46247436 46903428 47103870 47969415 48106080 48166820 48303216 48907848 49197720 50019390 50101389 50244128 51089940 51167376 51386040 52114920 52242474 52262496 52983502 53354016 53670240 54119340 55021329 55347435 55668210 55734480 56524644 56525040 56852640 57800184 57809295 58629285 59037264 59039280 59379424 60023268 60379020 61134810 61235031 61307928 61663248 62537904 62805160 63959220 64943208 65025207 65210464 65328120 65596960 66416922 66692520 66801852 67830048 68119920 68514720 69371154 69486560 69656632 70355142 70655805 72159120 72250230 72454824 73361772 73796580 74224280 75029085 75366192 76634910 76751064 77066912 77079060 78172380 78363711 79475253 80031024 80505360 81179010 81513080 81646708 81743904 83502315 84786966 84787560 85278960 86590944 86700276 87070790 87104160 88555896 88923360 89069136 90034902 90568530 91702215 92494872 93806856 94207740 95777869 95938830 96333640 96606432 97815696 98395440 99625383 100038780 100202778 102058385 102179880 102334752 102772080 104229840 104484948 105532713 105967004 108238680 108375345 110042658 110694870 111336420 111468960 113049288 113050080 113192027 115600368 115618590 117258570 118074528 118078560 120046536 120758040 122269620 122470062 122615856 123326496 125075808 125610320 127180449 127918440 129886416 130050414 130606185 130656240 132458755 132833844 133385040 133603704 136239840 138742308 139313264 140710284 141311610 144318240 144500460 144909648 146723544 147593160 148448560 150058170 150304167 150732384 153269820 153502128 154158120 156344760 156727422 158950506 160062048 161010720 162358020 163026160 163293416 165063987 166042305 167004630 169573932 169575120 170557920 173400552 173427885 174141580 175887855 177111792 178138272 180069804 181137060 183404430 183705093 184989744 187613712 188415480 191555738 191877660 192667280 195075621 195631392 196790880 199250766 200077560 200405556 204116770 204359760 205544160 208459680 208969896 211065426 211934008 211967415 216477360 216750690 220085316 221389740 222672840 225087255 226098576 226384054 231200736 231237180 234517140 235091133 238425759 240093072 241516080 244539240 244940124 245231712 250506945 251220640 254360898 255836880 259772832 260100828 261212370 261312480 264917510 265667688 266770080 267207408 275106645 277484616 278626528 281420568 282623220 287333607 289000920 289819296 293447088 295186320 296897120 300116340 300608334 306175155 306539640 307004256 308316240 312689520 313454844 317901012 324716040 325126035 326052320 326586832 330127974 332084610 334009260 339147864 339150240 339576081 346801104 346855770 348283160 351775710 354223584 360139608 362274120 366808860 367410186 369979488 375227424 376830960 381541347 383111476 383755320 385334560 390151242 391818555 397376265 398501532 400155120 400811112 408233540 408719520 417939792 422130852 423868016 423934830 432954720 433501380 440170632 442779480 445345680 450174510 450912501 452197152 452768108 462474360 469034280 470182266 476851518 478889345 480186144 483032160 489078480 489880248 495191961 498126915 501013890 508721796 511673760 520201656 522424740 527663565 529835020 531335376 534414816 550213290 551115279 554969232 562841136 565246440 565960135 574667214 578001840 585226863 586894176 590372640 600232680 601216668 612350310 613079280 616632480 625379040 626909688 635802024 635902245 649432080 650252070 653173664 660255948 664169220 668018520 678295728 679152162 693602208 693711540 696566320 703551420 705273399 715277277 720279216 724548240 733617720 734820372 751520835 753661920 763082694 766222952 767510640 780302484 783637110 794752530 797003064 800310240 801622224 816467080 825319935 835879584 844261704 847736032 847869660 862000821 867002760 880341264 885558960 890691360 900349020 901825002 905536216 918525465 924948720 938068560 940364532 953703036 957778690 975378105 978156960 979760496 990383922 996253830 1002027780 1017443592 1018728243 1040403312 1044849480 1055327130 1059670040 1062670752 1100426580 1102230558 1109938464 1125682272 1130492880 1131920270 1149334428 1156003680 1170453726 1175455665 1192128795 1200465360 1202433336 1224700620 1226158560 1245112297 1253819376 1271604048 1271804490 1298864160 1300504140 1320511896 1328338440 1336037040 1356591456 1358304324 1387423080 1393132640 1407102840 1410546798 1430554554 1436668035 1440558432 1449096480 1467235440 1469640744 1503041670 1526165388 1532445904 1535021280 1560604968 1567274220 1589505060 1594006128 1603244448 1632934160 1650639870 1653345837 1688523408 1695739320 1697880405 1724001642 1734005520 1760682528 1771117920 1800698040 1803650004 1811072432 1837050930 1849897440 1876137120 1880729064 1907406072 1907706735 1915557380 1950756210 1959520992 1980767844 1992507660 2004055560 2034887184 2037456486 2080806624 2089698960 2110654260 2115820197 2119340080 2145831831 2200853160 2204461116 2254562505 2260985760 2263840540 2298668856 2340907452 2350911330 2384257590 2400930720 2404866672 2449401240 2475959805 2490224594 2507638752 2543208096 2543608980 2586002463 2601008280 2641023792 2656676880 2672074080 2716608648 2755576395 2774846160 2814205680 2821093596 2861109108 2873336070 2926134315 2934470880 2939281488 3006083340 3052330776 3056184729 3064891808 3121209936 3134548440 3179010120 3188012256 3265868320 3301279740 3306691674 3377046816 3391478640 3395760810 3448003284 3468011040 3526366995 3576386385 3601396080 3607300008 3622144864 3674101860 3735336891 3761458128 3814812144 3815413470 3831114760 3901512420 3961535688 3985015320 4008111120 4069774368 4074912972 4179397920 4221308520 4231640394 4238680160 4291663662 4310004105 4401706320 4408922232 4509125010 4527681080 4597337712 4681814904 4701822660 4768515180 4809733344 4898802480 4951919610 4960037511 4980449188 5087217960 5093641215 5172004926 5202016560 5282047584 5313353760 5433217296 5511152790 5549692320 5628411360 5642187192 5722218216 5746672140 5852268630 5878562976 6012166680 6104661552 6112369458 6225561485 6242419872 6269096880 6358020240 6437495493 6602559480 6613383348 6782957280 6791521620 6896006568 7052733990 7152772770 7202792160 7214600016 7348203720 7470673782 7522916256 7629624288 7630826940 7662229520 7758007389 7803024840 7923071376 7970030640 8016222240 8149825944 8266729185 8442617040 8463280788 8583327324 8620008210 8803412640 8817844464 9018250020 9055362160 9168554187 9194675424 9363629808 9403645320 9537030360 9797604960 9903839220 9920075022 9960898376 10174435920 10187282430 10344009852 10404033120 10579100985 10729159155 10866434592 11022305580 11206010673 11284374384 11444436432 11493344280 11704537260 12024333360 12209323104 12224738916 12451122970 12538193760 12716040480 12874990986 12930012315 13205118960 13226766696 13583043240 13792013136 14105467980 14305545540 14429200032 14696407440 14941347564 15261653880 15280923645 15324459040 15516014778 15606049680 15846142752 15940061280 16299651888 16533458370 16885234080 16926561576 17166654648 17240016420 17635688928 18036500040 18110724320 18337108374 18676684455 18727259616 18807290640 19074060720 19807678440 19840150044 19921796752 20348871840 20374564860 20688019704 21158201970 21458318310 22044611160 22412021346 22568748768 22888872864 22986688560 23274022167 23409074520 24048666720 24449477832 24800187555 24902245940 25749981972 25860024630 26410237920 26453533392 27166086480 27505662561 27584026272 28210935960 28611091080 29392814880 29882695128 30523307760 30561847290 31032029556 31212099360 32187477465 32599303776 33066916740 33618032019 33853123152 34333309296 34480032840 36073000080 36674216748 37353368910 37614581280 38148121440 38790036945 39615356880 39680300088 39843593504 40749129720 41376039408 42316403940 42916636620 44089222320 44824042692 45842770935 45973377120 46548044334 46818149040 48898955664 49600375110 49804491880 51499963944 51720049260 52907066784 54332172960 55011325122 56030053365 56421871920 57222182160 59765390256 61046615520 61123694580 62064059112 64374954930 66133833480 67236064038 67706246304 68666618592 68960065680 72146000160 73348433496 74706737820 77580073890 79230713760 79360600176 81498259440 82752078816 84632807880 85833273240 88178444640 89648085384 91685541870 93096088668 93636298080 97797911328 99200750220 99608983760 100854096057 102999927888 103440098520 110022650244 112060106730 112843743840 114444364320 116370110835 119530780512 122247389160 124128118224 128749909860 132267666960 134472128076 137528312805 137920131360 146696866992 149413475640 155160147780 158721200352 162996518880 168090160095 169265615760 171666546480 179296170768 183371083740 186192177336 198401500440 199217967520 201708192114 205999855776 206880197040 220045300488 224120213460 232740221670 244494778320 248256236448 257499819720 264535333920 268944256152 275056625610 293393733984 298826951280 302562288171 310320295560 336180320190 338531231520 343333092960 358592341536 366742167480 372384354672 396803000880 403416384228 413760394080 440090600976 448240426920 465480443340 488989556640 504270480285 514999639440 537888512304 550113251220 597653902560 605124576342 620640591120 672360640380 733484334960 744768709344 793606001760 806832768456 880181201952 896480853840 930960886680 1008540960570 1029999278880 1075777024608 1100226502440 1210249152684 1241281182240 1344721280760 1466968669920 1512811440855 1613665536912 1792961707680 1861921773360 2017081921140 2200453004880 2420498305368 2689442561520 3025622881710 3227331073824 3723843546720 4034163842280 4400906009760 4840996610736 5378885123040 6051245763420 8068327684560 9681993221472 12102491526840 16136655369120 24204983053680 48409966107360
- Sum of all divisors σ(n): 208988871856128
- Sum of proper divisors (its aliquot sum) s(n): 160578905748768
- 48409966107360 is an abundant number, because the sum of its proper divisors (160578905748768) is greater than itself. Its abundance is 112168939641408
Bases of 48409966107360
- Binary: 10110000000111010100101101010101011010111000002
- Hexadecimal: 0x2C0752D55AE0
- Base-36: H5R8BWU00
Squares and roots of 48409966107360
- 48409966107360 squared (484099661073602) is 2343524818515743911046169600
- 48409966107360 cubed (484099661073603) is 113449957036104157714302361056150368256000
-
The
square root of 48409966107360 is 6957727.0791085219 -
The
cube root of 48409966107360 is 36445.5850479529
Scales and comparisons
How big is 48409966107360?- 48,409,966,107,360 seconds is equal to 1,539,287 years, 9 weeks, 2 days, 15 hours, 36 minutes.
-
To count from 1 to 48,409,966,107,360 would take you about three million, eight hundred forty-eight thousand, two hundred seventeen 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 48409966107360 cubic inches would be around 3037.1 feet tall.
Recreational maths with 48409966107360
- 48409966107360 backwards is 06370166990484
- The number of decimal digits it has is: 14
- The sum of 48409966107360'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 48409966107360 - Facts about the integer". Numbermatics.com. 2024. Web. 25 September 2024.
APA style:
Numbermatics. (2024). Number 48409966107360 - Facts about the integer. Retrieved 25 September 2024, from https://numbermatics.com/n/48409966107360/
Chicago style:
Numbermatics. 2024. "Number 48409966107360 - Facts about the integer". https://numbermatics.com/n/48409966107360/
The information we have on file for 48409966107360 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 48409966107360, math, Factors of 48409966107360, curriculum, school, college, exams, university, Prime factorization of 48409966107360, STEM, science, technology, engineering, physics, economics, calculator, forty-eight trillion, four hundred nine billion, nine hundred sixty-six million, one hundred seven thousand, three hundred sixty.