931805390919312
931,805,390,919,312 is an even composite number composed of eight prime numbers multiplied together.
What does the number 931805390919312 look like?
This visualization shows the relationship between its 8 prime factors (large circles) and 2160 divisors.
931805390919312 is an even composite number. It is composed of eight distinct prime numbers multiplied together. It has a total of two thousand, one hundred sixty divisors.
Prime factorization of 931805390919312:
24 × 32 × 7 × 13 × 292 × 31 × 612 × 733
(2 × 2 × 2 × 2 × 3 × 3 × 7 × 13 × 29 × 29 × 31 × 61 × 61 × 733)See below for interesting mathematical facts about the number 931805390919312 from the Numbermatics database.
Names of 931805390919312
- Cardinal: 931805390919312 can be written as Nine hundred thirty-one trillion, eight hundred five billion, three hundred ninety million, nine hundred nineteen thousand, three hundred twelve.
Scientific notation
- Scientific notation: 9.31805390919312 × 1014
Factors of 931805390919312
Divisors of 931805390919312
- Number of divisors d(n): 2160
-
Complete list of divisors:
1 2 3 4 6 7 8 9 12 13 14 16 18 21 24 26 28 29 31 36 39 42 48 52 56 58 61 62 63 72 78 84 87 91 93 104 112 116 117 122 124 126 144 156 168 174 182 183 186 203 208 217 232 234 244 248 252 261 273 279 312 336 348 364 366 372 377 403 406 427 434 464 468 488 496 504 522 546 549 558 609 624 651 696 728 732 733 744 754 793 806 812 819 841 854 868 899 936 976 1008 1044 1092 1098 1116 1131 1209 1218 1281 1302 1392 1456 1464 1466 1488 1508 1586 1612 1624 1638 1682 1708 1736 1769 1798 1827 1872 1891 1953 2088 2184 2196 2199 2232 2262 2379 2418 2436 2523 2562 2604 2639 2697 2821 2928 2932 3016 3172 3224 3248 3276 3364 3393 3416 3472 3538 3596 3627 3654 3721 3782 3843 3906 4176 4368 4392 4398 4464 4524 4758 4836 4872 5046 5124 5131 5208 5278 5307 5394 5551 5642 5673 5864 5887 6032 6293 6344 6448 6552 6597 6728 6786 6832 7076 7137 7192 7254 7308 7442 7564 7569 7686 7812 7917 8091 8463 8784 8796 9048 9516 9529 9672 9744 10092 10248 10262 10416 10556 10614 10788 10933 11102 11163 11284 11346 11687 11728 11774 12383 12586 12688 13104 13194 13237 13456 13572 14152 14274 14384 14508 14616 14884 15128 15138 15372 15393 15624 15834 15921 16182 16653 16926 17019 17592 17661 18096 18879 19032 19058 19344 20184 20496 20524 21112 21228 21257 21576 21866 22204 22326 22568 22692 22723 22997 23374 23548 23751 24583 24766 25172 25389 26047 26071 26388 26474 27144 28304 28548 28587 29016 29232 29768 30256 30276 30744 30786 31248 31668 31842 32364 32799 33306 33489 33852 34038 35061 35184 35322 37149 37758 38064 38116 39711 40368 41048 42224 42456 42514 43152 43732 44408 44652 44713 45136 45384 45446 45994 46179 46748 47096 47502 48373 49166 49532 49959 50344 50778 51301 52094 52142 52776 52948 52983 54288 54839 56637 57096 57174 58032 59536 60552 61488 61572 63336 63684 63771 64728 65598 66612 66703 66978 67704 68076 68169 68991 70122 70644 73749 74298 75516 76232 76531 78141 78213 79422 81809 82096 84912 85028 85761 87464 88816 89304 89426 90768 90892 91988 92358 93496 94192 95004 96746 98332 98397 99064 99918 100688 101556 102602 104188 104284 105183 105552 105896 105966 107909 109678 111447 113274 114192 114348 115351 119133 121104 123144 126672 127368 127542 129456 131196 133224 133406 133956 134139 135408 136152 136338 137982 140244 141288 145119 147498 148596 148799 151032 152464 153062 153903 156282 156426 158844 159061 160979 163618 164517 170056 171522 172081 174928 178608 178852 181784 182497 183976 184716 186992 190008 191313 193492 196664 196794 198128 199836 200109 203112 204507 205204 206973 208376 208568 210366 211792 211932 215818 219356 221247 222894 226548 228696 229593 230702 234423 234639 238266 245427 246288 254736 255084 262392 266448 266812 267912 268278 272304 272676 275964 276341 280488 282576 290238 294996 295399 297192 297598 302064 306124 307806 312564 312852 312991 317688 318122 321958 323727 327236 329034 338611 338923 340112 343044 344162 346053 357704 359107 363568 364994 367952 369432 380016 382626 383873 386984 393328 393588 399672 400218 402417 406224 409014 410408 413946 416752 417136 420732 423864 431636 435357 438712 442494 445788 446397 453096 457392 459186 461404 461709 468846 469278 476532 477183 482937 490854 493551 510168 516243 524784 533624 535824 536556 545352 547491 551928 552682 560976 580476 581269 589992 590798 594384 595196 600327 612248 615612 616453 625128 625704 625982 635376 636244 643916 647454 654472 658068 658967 666913 677222 677846 686088 688324 688779 692106 712907 715408 718214 729988 736281 738864 755363 765252 767746 773968 787176 799344 800436 804834 807457 818028 820816 827892 829023 841464 847728 863272 870714 877424 884988 886197 891576 892794 906192 918372 922808 923418 937692 938556 938973 953064 954366 965874 971181 981708 987102 1015833 1016769 1020336 1032486 1038159 1067248 1073112 1077321 1090704 1094982 1103856 1105364 1151619 1160952 1162538 1179984 1181596 1190392 1200654 1224496 1231224 1232906 1250256 1251408 1251964 1272488 1287832 1294908 1296677 1308944 1316136 1317934 1333826 1339191 1354444 1355692 1372176 1376648 1377558 1384212 1386103 1402817 1425814 1431549 1436428 1448811 1459976 1472562 1499563 1510726 1530504 1535492 1548729 1574352 1590331 1600872 1609668 1614914 1636056 1642473 1655784 1658046 1682928 1726544 1741428 1743807 1769976 1772394 1783152 1785588 1836744 1845616 1846836 1849359 1875384 1877112 1877946 1906128 1908732 1931748 1934387 1942362 1963416 1974204 1976901 2000739 2031666 2033538 2064972 2067793 2076318 2138721 2146224 2154642 2189964 2210728 2266089 2303238 2321904 2325076 2363192 2372461 2380784 2401308 2422371 2462448 2465812 2487069 2503928 2544976 2575664 2589816 2593354 2632272 2635868 2658591 2667652 2678382 2708888 2711384 2727493 2753296 2755116 2768424 2772206 2805634 2816919 2851628 2863098 2872856 2897622 2919952 2945124 2999126 3021452 3047499 3050307 3061008 3070984 3097458 3129361 3180662 3201744 3219336 3229828 3231963 3272112 3284946 3311568 3316092 3345179 3454857 3482856 3487614 3539952 3544788 3571176 3673488 3693672 3698718 3750768 3754224 3755892 3817464 3863496 3868774 3884724 3890031 3926832 3948408 3953802 4001478 4063332 4067076 4068883 4129944 4135586 4152636 4158309 4208451 4277442 4309284 4315171 4379928 4421456 4498689 4532178 4606476 4612769 4650152 4668391 4726384 4744922 4770993 4802616 4844742 4931624 4974138 4990349 5007856 5179632 5186708 5231421 5271736 5317182 5335304 5356764 5417776 5422768 5454986 5510232 5536848 5544412 5548077 5611268 5633838 5703256 5726196 5745712 5795244 5803161 5890248 5930703 5998252 6002217 6042904 6094998 6100614 6141968 6194916 6203379 6258722 6361324 6416163 6438672 6459656 6463926 6569892 6632184 6690358 6798267 6909714 6965712 6975228 7089576 7117383 7142352 7267113 7387344 7397436 7511784 7634928 7726992 7737548 7769448 7780062 7896816 7907604 8002956 8013889 8126664 8134152 8137766 8182479 8259888 8271172 8305272 8316618 8416902 8554884 8566571 8618568 8630342 8759856 8997378 9064356 9076739 9212952 9225538 9300304 9336782 9388083 9489844 9541986 9605232 9689484 9702721 9819719 9863248 9948276 9980698 10035537 10373416 10462842 10496941 10543472 10634364 10670608 10713528 10909972 11020464 11088824 11096154 11132317 11222536 11267676 11406512 11452392 11590488 11606322 11670093 11780496 11861406 11996504 12004434 12085808 12189996 12201228 12206649 12389832 12406758 12474927 12517444 12625353 12722648 12832326 12919312 12927852 12945513 13139784 13264368 13380716 13496067 13596534 13819428 13838307 13950456 14005173 14179152 14234766 14312979 14534226 14794872 14971047 15023568 15475096 15538896 15560124 15815208 16005912 16027778 16253328 16268304 16275532 16364958 16542344 16610544 16633236 16833804 16856801 17109768 17133142 17237136 17260684 17409483 17994756 18019339 18128712 18153478 18425904 18451076 18610137 18673564 18776166 18979688 19083972 19092451 19110043 19378968 19405442 19639438 19896552 19961396 20071074 20674303 20746832 20925684 20993882 21268728 21352149 21427056 21819944 21905527 22177648 22192308 22264634 22445072 22535352 22904784 23180976 23212644 23340186 23416253 23722812 23993008 24008868 24041667 24379992 24402456 24413298 24547437 24779664 24813516 24949854 25034888 25250706 25445296 25664652 25699713 25855704 25891026 26279568 26761432 26992134 27193068 27230217 27638856 27676614 27900912 28010346 28164249 28469532 28625958 29068452 29108163 29459157 29589744 29942094 30106611 30950192 31120248 31490823 31630416 32011824 32055556 32551064 32729916 33084688 33266472 33396951 33667608 33713602 34219536 34266284 34521368 34818966 35457409 35989512 36038678 36257424 36306956 36619947 36902152 37220274 37347128 37552332 37603633 37959376 38167944 38184902 38220086 38757936 38810884 38836539 39278876 39793104 39922792 40142148 40196987 40681693 41348606 41514921 41851368 41987764 42015519 42537456 42704298 43487327 43639888 43811054 44384616 44529268 44913141 45070704 46425288 46680372 46832506 47445624 48017736 48083334 48759984 48804912 48826596 49094874 49627032 49899708 50069776 50501412 50570403 51329304 51399426 51711408 51782052 53522864 53984268 54058017 54386136 54460434 55277712 55353228 56020692 56097223 56328498 56939064 57251916 57277353 57330129 58136904 58216326 58918314 59884188 59965997 60213222 62022909 62240496 62981646 64111112 65102128 65459832 65716581 66532944 66793902 67335216 67427204 68532568 69042736 69637932 70248759 70914818 71979024 72077356 72125001 72613912 73239894 73804304 74440548 74694256 75104664 75207266 76335888 76369804 76440172 77099139 77621768 77673078 78557752 79097297 79845584 80284296 80393974 81363386 81690651 82697212 83029842 83702736 83975528 84031038 84552283 85408596 86974654 87324489 87622108 88377471 88769232 89058536 89826282 92850576 93360744 93665012 94472469 94891248 96035472 96166668 97010191 97653192 98189748 99254064 99799416 100190853 101002824 101140806 102658608 102798852 103564104 106372227 107968536 108116034 108772272 108920868 110706456 112041384 112194446 112656996 112810899 113878128 114503832 114554706 114660258 116273808 116432652 117836628 117997607 119768376 119931994 120426444 120590961 122045079 124045818 125963292 126135373 128222224 130461981 130919664 131433162 133587804 133770301 134854408 137065136 139275864 140497518 141829636 144154712 144250002 144720121 145227824 146479788 148881096 150209328 150414532 151711209 152739608 152880344 154198278 155243536 155346156 157115504 158194594 160568592 160787948 162174051 162726772 163381302 165394424 166059684 167951056 168062076 168291669 169104566 170817192 171832059 171990387 173949308 174648978 175244216 176754942 178117072 179652564 179897991 186068727 186721488 187330024 188944938 192333336 194020382 195306384 196379496 197149743 199598832 200381706 202005648 202281612 205597704 207128208 210746277 212744454 215937072 216232068 217841736 221412912 224082768 224388892 225313992 225621798 229007664 229109412 229320516 232865304 235673256 235995214 237291891 239536752 239863988 240852888 241181922 244090158 248091636 248201863 248430559 251926584 252270746 253656849 260923962 262866324 263225431 267175608 267540602 269708816 278551728 280995036 281378909 283659272 284771851 288309424 288500004 289440242 291030573 292959576 297762192 300829064 303422418 304411289 305479216 305760688 308396556 310692312 316389188 319116681 321575896 324348102 325453544 326762604 330788848 332119368 336124152 336583338 338209132 338432697 341634384 343664118 343980774 347898616 349297956 350488432 353509884 353992821 359305128 359795982 361772883 366135237 372137454 374660048 377889876 378406119 384666672 388040764 391385943 392758992 394299486 400763412 401310903 404563224 411195408 421492554 425488908 432464136 434160363 435683472 448777784 450627984 451243596 458218824 458641032 465730608 471346512 471990428 474583782 479727976 481705776 482363844 488180316 488847229 496183272 496403726 496861118 503853168 504541492 504875007 507313698 521847924 522560831 525732648 526450862 534351216 535081204 539693973 553681079 561990072 562757818 567318544 569543702 577000008 578880484 582061146 585919152 591865981 601658128 606844836 608822578 616793112 621384624 632778376 638233362 643151792 648696204 650907088 653525208 664238736 672248304 673166676 676418264 676865394 679071337 687328236 687961548 695797232 698595912 707019768 707985642 711875673 718610256 719591964 723545766 732270474 744274908 744605589 745291677 755779752 756812238 760970547 776081528 782771886 788598972 789676293 801526824 802621806 809126448 842985108 844136727 850977816 854315553 864928272 868320726 873091719 897555568 902487192 913233867 916437648 917282064 943980856 949167564 959455952 964727688 976360632 977694458 992366544 992807452 993722236 1009082984 1009750014 1014627396 1028264861 1043695848 1045121662 1051465296 1052901724 1061978463 1070162408 1079387946 1099179679 1107362158 1123980144 1125515636 1135218357 1139087404 1154000016 1157760968 1164122292 1165712623 1183731962 1203932709 1213689672 1217645156 1233586224 1261132483 1265556752 1276466724 1297392408 1302481089 1307050416 1346333352 1352836528 1353730788 1358142674 1374656472 1375923096 1397191824 1414039536 1415971284 1423751346 1439183928 1447091532 1464540948 1466541687 1488549816 1489211178 1490583354 1511559504 1513624476 1521941094 1552163056 1565543772 1567682493 1577197944 1579352586 1603053648 1605243612 1661043237 1685970216 1688273454 1701955632 1708631106 1736641452 1739013913 1746183438 1775597943 1804974384 1826467734 1887961712 1898335128 1929455376 1952721264 1955388916 1985614904 1987444472 2018165968 2019500028 2029254792 2037214011 2056529722 2087391696 2090243324 2105803448 2123956926 2140324816 2158775892 2198359358 2214724316 2233816767 2235875031 2251031272 2270436714 2278174808 2293821613 2315521936 2328244584 2331425246 2367463924 2369028879 2407865418 2427379344 2435290312 2452016207 2522264966 2532410181 2552933448 2562946659 2594784816 2604962178 2692666704 2707461576 2716285348 2739701601 2749312944 2751846192 2831942568 2847502692 2878367856 2894183064 2929081896 2933083374 2977099632 2978422356 2981166708 3027248952 3043882188 3084794583 3131087544 3135364986 3154395888 3158705172 3210487224 3297539037 3322086474 3371940432 3376546908 3417262212 3421930603 3473282904 3478027826 3492366876 3497137869 3551195886 3652935468 3657925817 3783397449 3796670256 3910777832 3971229808 3974888944 4039000056 4058509584 4074428022 4113059444 4180486648 4211606896 4247913852 4317551784 4396718716 4399625061 4429448632 4467633534 4471750062 4502062544 4540873428 4556349616 4587643226 4656489168 4662850492 4703047479 4734927848 4738057758 4815730836 4870580624 4904032414 4983129711 5044529932 5064820362 5105866896 5125893318 5209924356 5217041739 5326793829 5414923152 5432570696 5479403202 5663885136 5695005384 5788366128 5858163792 5866166748 5956844712 5962333416 6054497904 6087764376 6111642033 6169589166 6262175088 6270729972 6317410344 6420974448 6595078074 6644172948 6753093816 6834524424 6843861206 6881464839 6946565808 6956055652 6984733752 6994275738 7102391772 7197854027 7305870936 7315851634 7356048621 7566794898 7694257753 7821555664 8078000112 8148856044 8159988361 8226118888 8360973296 8495827704 8635103568 8793437432 8799250122 8827927381 8858897264 8935267068 8943500124 9081746856 9175286452 9254383749 9325700984 9406094958 9469855696 9476115516 9631461672 9808064828 9892617111 9966259422 10089059864 10129640724 10251786636 10265791809 10419848712 10434083478 10491413607 10653587658 10865141392 10958806404 10973777451 11350192347 11390010768 11732333496 11913689424 11924666832 12175528752 12223284066 12339178332 12541459944 12634820688 13190156148 13288345896 13506187632 13669048848 13687722412 13762929678 13912111304 13969467504 13988551476 14204783544 14395708054 14611741872 14631703268 14712097242 15133589796 15154264099 15388515506 15651125217 16056751291 16297712088 16319976722 16452237776 16991655408 17164113449 17586874864 17598500244 17655854762 17870534136 17887000248 18163493712 18350572904 18508767498 18651401968 18812189916 18952231032 19262923344 19616129656 19785234222 19932518844 20178119728 20259281448 20503573272 20531583618 20644394517 20839697424 20868166956 20982827214 21307175316 21593562081 21917612808 21947554902 22068145863 22700384694 23082773259 23464666992 24446568132 24479965083 24678356664 25082919888 26380312296 26483782143 26576691792 27375444824 27525859356 27824222608 27977102952 28409567088 28791416108 29263406536 29424194484 29819680969 30267179592 30308528198 30777031012 30797375427 31302250434 31876210691 32113502582 32595424176 32639953444 32921332353 34328226898 35197000488 35311709524 35741068272 35774000496 36701145808 37017534996 37624379832 37904462064 39232259312 39570468444 39865037688 40518562896 41007146544 41063167236 41288789034 41736333912 41965654428 42614350632 43187124162 43835225616 43895109804 44136291726 45400769388 45462792297 46165546518 48170253873 48893136264 48959930166 49356713328 51492340347 52760624592 52967564286 54750889648 55051718712 55954205904 57582832216 58526813072 58848388968 59639361938 60534359184 60617056396 61554062024 61594750854 62604500868 63752421382 64227005164 64780686243 65279906888 65842664706 68656453796 69248319777 70394000976 70623419048 71108470003 73439895249 74035069992 75248759664 79140936888 79451346429 79730075376 82126334472 82577578068 83472667824 83931308856 85228701264 86374248324 87790219608 88272583452 89459042907 90801538776 90925584594 92331093036 95628632073 96340507746 97786272528 97919860332 102984680694 105935128572 106079848693 110103437424 115165664432 117696777936 119278723876 121234112792 123108124048 123189501708 125209001736 127504842764 128454010328 129561372486 130559813776 131685329412 136388376891 137312907592 138496639554 141246838096 142216940006 144510761619 146879790498 148070139984 154477021041 158281873776 158902692858 164252668944 165155156136 167862617712 172748496648 175580439216 176545166904 178918085814 181603077552 181851169188 184662186072 191257264146 192681015492 195839720664 205969361388 208737766783 211870257144 212159697386 213325410009 223133474837 238557447752 242468225584 246379003416 250418003472 255009685528 256908020656 259122744972 263370658824 268377128721 272776753782 274625815184 276993279108 284433880012 286885896219 289021523238 293759580996 308954042082 317805385716 318239546079 330310312272 345496993296 353090333808 357836171628 363702338376 369324372144 382514528292 385362030984 391679441328 411938722776 417475533566 423740514288 424319394772 426650820018 446266949674 477114895504 492758006832 497759290021 510019371056 518245489944 526741317648 536754257442 545553507564 553986558216 568867760024 573771792438 578043046476 587519161992 617908084164 626213300349 635610771432 636479092158 639976230027 669400424511 715672343256 727404676752 765029056584 770724061968 823877445552 834951067132 848638789544 853301640036 892533899348 924410110039 954718638237 995518580042 1036490979888 1073508514884 1091107015128 1107973116432 1137735520048 1147543584876 1156086092952 1175038323984 1235816168328 1252426600698 1271221542864 1272958184316 1279952460054 1338800849022 1431344686512 1493277870063 1530058113168 1669902134264 1697277579088 1706603280072 1785067798696 1848820220078 1878639901047 1909437276474 1991037160084 2008201273533 2147017029768 2182214030256 2295087169752 2312172185904 2471632336656 2504853201396 2545916368632 2559904920108 2677601698044 2773230330117 2986555740126 3339804268528 3413206560144 3570135597392 3697640440156 3757279802094 3818874552948 3982074320168 4016402547066 4294034059536 4479833610189 4590174339504 5009706402792 5091832737264 5119809840216 5355203396088 5546460660234 5973111480252 6470870770273 7395280880312 7514559604188 7637749105896 7964148640336 8032805094132 8319690990351 8959667220378 10019412805584 10239619680432 10710406792176 11092921320468 11946222960504 12941741540546 14790561760624 15029119208376 15275498211792 16065610188264 16639381980702 17919334440756 19412612310819 22185842640936 23892445921008 25883483081092 30058238416752 32131220376528 33278763961404 35838668881512 38825224621638 44371685281872 51766966162184 58237836932457 66557527922808 71677337763024 77650449243276 103533932324368 116475673864914 133115055845616 155300898486552 232951347729828 310601796973104 465902695459656 931805390919312
- Sum of all divisors σ(n): 3493201221479424
- Sum of proper divisors (its aliquot sum) s(n): 2561395830560112
- 931805390919312 is an abundant number, because the sum of its proper divisors (2561395830560112) is greater than itself. Its abundance is 1629590439640800
Bases of 931805390919312
- Binary: 110100111101111000110110010101001101010110100100002
- Hexadecimal: 0x34F78D9535690
- Base-36: 96APHJ91G0
Squares and roots of 931805390919312
- 931805390919312 squared (9318053909193122) is 868261286546291854228494553344
- 931805390919312 cubed (9318053909193123) is 809050547530372254140650173486087508983779328
-
The
square root of 931805390919312 is 30525487.5623520877 -
The
cube root of 931805390919312 is 97673.1227375677
Scales and comparisons
How big is 931805390919312?- 931,805,390,919,312 seconds is equal to 29,628,529 years, 8 weeks, 5 days, 2 hours, 55 minutes, 12 seconds.
-
To count from 1 to 931,805,390,919,312 would take you about seventy-four million, seventy-one thousand, three hundred twenty-two 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 931805390919312 cubic inches would be around 8139.4 feet tall.
Recreational maths with 931805390919312
- 931805390919312 backwards is 213919093508139
- 931805390919312 is a
Harshad number . - The number of decimal digits it has is: 15
- The sum of 931805390919312'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 931805390919312 - Facts about the integer". Numbermatics.com. 2024. Web. 21 September 2024.
APA style:
Numbermatics. (2024). Number 931805390919312 - Facts about the integer. Retrieved 21 September 2024, from https://numbermatics.com/n/931805390919312/
Chicago style:
Numbermatics. 2024. "Number 931805390919312 - Facts about the integer". https://numbermatics.com/n/931805390919312/
The information we have on file for 931805390919312 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 931805390919312, math, Factors of 931805390919312, curriculum, school, college, exams, university, Prime factorization of 931805390919312, STEM, science, technology, engineering, physics, economics, calculator, nine hundred thirty-one trillion, eight hundred five billion, three hundred ninety million, nine hundred nineteen thousand, three hundred twelve.