34166880748000
34,166,880,748,000 is an even composite number composed of eight prime numbers multiplied together.
What does the number 34166880748000 look like?
This visualization shows the relationship between its 8 prime factors (large circles) and 2304 divisors.
34166880748000 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 34166880748000:
25 × 53 × 7 × 11 × 132 × 67 × 97 × 101
(2 × 2 × 2 × 2 × 2 × 5 × 5 × 5 × 7 × 11 × 13 × 13 × 67 × 97 × 101)See below for interesting mathematical facts about the number 34166880748000 from the Numbermatics database.
Names of 34166880748000
- Cardinal: 34166880748000 can be written as Thirty-four trillion, one hundred sixty-six billion, eight hundred eighty million, seven hundred forty-eight thousand.
Scientific notation
- Scientific notation: 3.4166880748 × 1013
Factors of 34166880748000
Divisors of 34166880748000
- Number of divisors d(n): 2304
-
Complete list of divisors:
1 2 4 5 7 8 10 11 13 14 16 20 22 25 26 28 32 35 40 44 50 52 55 56 65 67 70 77 80 88 91 97 100 101 104 110 112 125 130 134 140 143 154 160 169 175 176 182 194 200 202 208 220 224 250 260 268 275 280 286 308 325 335 338 350 352 364 385 388 400 404 416 440 455 469 485 500 505 520 536 550 560 572 616 650 670 676 679 700 707 715 728 737 770 776 800 808 845 871 875 880 910 938 970 1000 1001 1010 1040 1067 1072 1100 1111 1120 1144 1183 1232 1261 1300 1313 1340 1352 1358 1375 1400 1414 1430 1456 1474 1540 1552 1616 1625 1675 1690 1742 1750 1760 1820 1859 1876 1925 1940 2000 2002 2020 2080 2134 2144 2200 2222 2275 2288 2345 2366 2425 2464 2522 2525 2600 2626 2680 2704 2716 2750 2800 2828 2860 2912 2948 3080 3104 3232 3250 3350 3380 3395 3484 3500 3535 3575 3640 3685 3718 3752 3850 3880 4000 4004 4040 4225 4268 4355 4400 4444 4550 4576 4690 4732 4850 5005 5044 5050 5159 5200 5252 5335 5360 5408 5432 5500 5555 5600 5656 5720 5896 5915 6097 6160 6305 6499 6500 6565 6700 6760 6767 6790 6968 7000 7070 7150 7280 7370 7436 7469 7504 7700 7760 7777 8008 8080 8375 8450 8536 8710 8800 8827 8888 9100 9191 9295 9380 9464 9581 9625 9700 9797 10010 10088 10100 10318 10400 10504 10670 10720 10864 11000 11110 11312 11323 11375 11440 11725 11792 11830 12125 12194 12320 12610 12625 12998 13000 13013 13130 13400 13520 13534 13580 13871 13936 14000 14140 14300 14443 14560 14740 14872 14938 15008 15400 15520 15554 16016 16160 16393 16750 16900 16975 17069 17072 17420 17654 17675 17776 17875 18200 18382 18425 18590 18760 18928 19162 19250 19400 19594 20020 20176 20200 20636 21008 21125 21340 21728 21775 22000 22220 22624 22646 22750 22880 23450 23584 23660 24250 24388 25025 25220 25250 25795 25996 26000 26026 26260 26675 26800 27040 27068 27160 27742 27775 27872 28000 28280 28600 28886 29480 29575 29744 29876 30485 30800 31108 31525 32032 32495 32786 32825 33500 33800 33835 33950 34138 34144 34840 35308 35350 35552 35750 36400 36764 36850 37180 37345 37520 37856 38324 38500 38800 38885 39188 40040 40352 40400 41272 42016 42250 42680 43550 44000 44135 44440 45292 45493 45500 45955 46475 46900 47320 47369 47905 48500 48776 48985 50050 50440 50500 51590 51992 52000 52052 52520 53350 53600 54136 54320 55484 55550 56560 56615 57200 57772 58625 58960 59150 59488 59752 60970 61600 62216 63050 64990 65065 65572 65650 67000 67067 67600 67670 67900 68276 68579 69355 69680 70616 70700 71489 71500 72215 72800 73528 73700 74360 74437 74690 75040 76648 77000 77600 77770 78376 79261 80080 80800 81965 82544 84487 84500 84875 85345 85360 87100 87971 88270 88375 88880 90584 90986 91000 91910 92125 92950 93800 94640 94738 95810 97000 97097 97552 97970 100100 100880 101000 101101 103180 103984 104104 105040 106700 107767 108272 108640 108875 110968 111100 113120 113230 114400 114751 115544 117250 117920 118300 119483 119504 121940 124432 124553 125125 126100 127361 128975 129980 130130 131144 131300 133375 134000 134134 135200 135340 135800 136552 137158 138710 138875 139360 141232 141400 142978 143000 144430 147056 147400 147875 148720 148874 149380 152425 153296 154000 155540 156752 157625 158522 160160 162475 163930 164125 165088 168974 169000 169175 169750 170690 170720 174200 175942 176540 176750 177760 180323 181168 181972 182000 183820 184250 185900 186725 187600 187759 189280 189476 191620 194000 194194 194425 195104 195940 200200 201760 202000 202202 206360 207968 208208 210080 213400 215534 216544 217750 220675 221936 222200 226460 227465 229502 229775 231088 232375 234500 236600 236845 238966 239008 239525 243880 244925 248864 249106 250250 252200 254722 257950 259960 260260 262288 262600 266750 268000 268268 270680 271600 273104 274316 277420 277750 282464 282800 283075 285956 286000 288860 294112 294800 295750 297440 297748 298760 304850 306592 308000 311080 313504 315250 317044 324950 325325 327860 328250 335335 337948 338000 338350 339500 341380 342895 346775 348400 351884 353080 353500 357445 360646 361075 362336 363944 364000 367640 368500 371800 372185 373450 375200 375518 378952 383240 388000 388388 388850 391880 396305 400400 404000 404404 409825 412720 416416 422435 426725 426800 431068 435500 439855 441350 443872 444400 452920 454930 459004 459550 462176 464750 469000 473200 473690 477932 479050 485485 487760 489850 498212 500423 500500 504400 505505 509444 515900 519920 520520 521059 524576 525200 533500 536536 538835 541360 543200 546208 548632 554840 555500 565600 566150 571912 572000 573755 577720 589600 591409 591500 595496 597415 597520 609700 615797 622160 622765 630500 634088 636805 644875 649900 650650 655720 656399 656500 670670 675896 676000 676700 679000 682760 685790 693550 696800 703768 706160 707000 714890 721292 722150 727888 735280 737000 743600 744370 746900 751036 754369 757904 762125 766480 776776 777700 783760 792610 800800 808808 812375 819650 825440 844870 845875 853450 853600 862136 871000 871871 879710 882700 888800 891527 901615 905840 909860 918008 919100 929357 929500 933625 938000 938795 946400 947380 955864 958100 967681 970970 972125 975520 979700 996424 1000846 1001000 1008800 1011010 1018888 1031800 1039840 1041040 1042118 1050400 1067000 1073072 1077670 1082720 1097264 1098331 1103375 1109680 1111000 1132300 1137325 1143623 1143824 1147510 1148875 1155440 1182818 1183000 1184225 1190992 1194830 1195040 1197625 1219400 1224625 1231594 1244320 1245530 1261000 1262261 1268176 1273610 1289750 1299800 1301300 1311440 1312798 1313000 1314313 1341340 1351792 1353400 1358000 1365520 1371580 1387100 1400971 1407536 1412320 1414000 1415375 1429780 1442584 1444300 1455776 1470560 1474000 1487200 1488740 1493800 1502072 1508738 1515808 1524250 1532960 1553552 1555400 1567520 1585220 1617616 1624750 1626625 1639300 1655693 1676675 1689740 1691750 1706900 1714475 1724272 1733875 1742000 1743742 1759420 1765400 1783054 1787225 1803230 1805375 1811680 1819720 1836016 1838200 1858714 1859000 1860925 1867250 1876000 1877590 1894760 1911728 1916200 1935362 1941940 1944250 1959400 1981525 1992848 2001692 2002000 2022020 2037776 2049125 2063600 2082080 2084236 2112175 2133625 2134000 2146144 2155340 2194528 2196662 2199275 2206750 2219360 2222000 2264600 2274650 2287246 2287648 2295020 2297750 2310880 2365636 2366000 2368450 2381984 2389660 2395250 2427425 2438800 2449250 2463188 2491060 2502115 2522000 2524522 2527525 2536352 2547220 2579500 2599600 2602600 2605295 2622880 2625596 2626000 2628626 2682680 2694175 2703584 2706800 2716000 2731040 2743160 2774200 2801942 2815072 2828000 2830750 2859560 2868775 2885168 2888600 2948000 2957045 2977480 2987075 2987600 3004144 3017476 3048500 3078985 3107104 3110800 3113825 3170440 3184025 3235232 3249500 3253250 3278600 3281995 3311386 3353350 3379480 3383500 3413800 3428950 3448544 3467750 3484000 3487484 3518840 3530800 3566108 3574450 3606460 3610750 3639440 3672032 3676400 3717428 3718000 3721850 3734500 3755180 3771845 3789520 3823456 3832400 3870724 3883880 3888500 3918800 3963050 3985696 4003384 4004000 4044040 4075552 4098250 4127200 4168472 4224350 4267250 4268000 4310680 4359355 4393324 4398550 4413500 4444000 4457635 4508075 4529200 4549300 4574492 4590040 4594793 4595500 4646785 4693975 4731272 4732000 4736900 4779320 4790500 4838405 4854850 4877600 4898500 4926376 4982120 5004230 5044000 5049044 5055050 5094440 5159000 5199200 5205200 5210590 5251192 5252000 5257252 5365360 5388350 5413600 5486320 5491655 5548400 5603884 5661500 5686625 5718115 5719120 5737550 5770336 5777200 5914090 5921125 5954960 5974150 5975200 6008288 6034952 6097000 6157970 6221600 6227650 6311305 6340880 6368050 6499000 6505499 6506500 6557200 6563990 6571565 6622772 6706700 6758960 6767000 6773767 6827600 6857900 6935500 6974968 7004855 7037680 7061600 7132216 7148900 7212920 7220389 7221500 7278880 7352800 7434856 7436000 7443700 7469000 7510360 7543690 7579040 7664800 7688317 7741448 7767760 7777000 7837600 7926100 8005361 8006768 8088080 8196500 8278465 8336944 8383375 8448700 8533187 8534500 8572375 8621360 8718710 8786648 8797100 8827000 8915270 8936125 9016150 9058400 9098600 9148984 9180080 9189586 9191000 9293570 9304625 9387950 9462544 9473800 9558640 9581000 9676810 9709700 9797000 9806797 9852752 9907625 9964240 10008460 10098088 10110100 10188880 10318000 10410400 10421180 10502384 10514504 10560875 10730720 10776700 10972640 10983310 10996375 11096800 11207768 11323000 11373250 11436230 11438240 11475100 11554400 11589851 11828180 11842250 11909920 11948300 12069904 12081641 12137125 12194000 12315940 12455300 12510575 12579853 12622610 12637625 12681760 12736100 12998000 13010998 13013000 13026475 13114400 13127980 13143130 13245544 13413400 13470875 13517920 13534000 13547534 13655200 13715800 13871000 13949936 14009710 14075360 14264432 14297800 14343875 14425840 14440778 14443000 14785225 14869712 14887400 14935375 14938000 15020720 15087380 15376634 15394925 15482896 15535520 15554000 15569125 15852200 15920125 16010722 16013536 16176160 16393000 16409975 16556930 16673888 16766750 16897400 17066374 17069000 17144750 17242720 17437420 17573296 17594200 17654000 17830540 17872250 18032300 18197200 18212623 18297968 18360160 18379172 18382000 18587140 18609250 18775900 18859225 18925088 18947600 19117280 19162000 19353620 19419400 19594000 19613594 19705504 19815250 19928480 20016920 20196176 20220200 20377760 20636000 20842360 21004768 21029008 21121750 21553400 21796775 21966620 21992750 22288175 22415536 22540375 22646000 22746500 22872460 22950200 22973965 23179702 23233925 23469875 23656360 23684500 23896600 24139808 24163282 24192025 24274250 24388000 24631880 24910600 25021150 25159706 25245220 25275250 25472200 25996000 26021996 26026000 26052950 26255960 26286260 26491088 26826800 26941750 27068000 27095068 27431600 27458275 27742000 27899872 28019420 28528864 28590575 28595600 28687750 28851680 28881556 28886000 29570450 29739424 29774800 29870750 29876000 30041440 30174760 30753268 30789850 30965792 31108000 31138250 31556525 31704400 31840250 32021444 32527495 32786000 32819950 32857825 33113860 33533500 33794800 33868835 34132748 34138000 34289500 34874840 35024275 35146592 35188400 35308000 35661080 35744500 36064600 36101945 36394400 36425246 36595936 36758344 36764000 37174280 37218500 37551800 37718450 37895200 38324000 38441585 38707240 38838800 39188000 39227188 39630500 40026805 40033840 40392352 40440400 41392325 41684720 42058016 42243500 42665935 43106800 43593550 43933240 43985500 44576350 44831072 45080750 45292000 45493000 45744920 45900400 45947930 46359404 46467850 46939750 47312720 47369000 47793200 48326564 48384050 48548500 49033985 49263760 49821200 50042300 50319412 50490440 50542723 50550500 50944400 52043992 52052000 52105900 52511920 52572520 52982176 53653600 53883500 54190136 54863200 54916550 55484000 56038840 57181150 57191200 57375500 57763112 57772000 57949255 59140900 59549600 59732309 59741500 60349520 60408205 61506536 61579700 62276500 62552875 62899265 63113050 63408800 63680500 64042888 65054990 65132375 65572000 65639900 65715650 66227720 67067000 67589600 67737670 68265496 68276000 68579000 69749680 70048550 70376800 71322160 71489000 72129200 72203890 72850492 73516688 73926125 74348560 74437000 75103600 75436900 76883170 76974625 77414480 77677600 78454376 79261000 80053610 80067680 80880800 82049875 82784650 83369440 84487000 84571487 85331870 86213600 87187100 87866480 87971000 88058971 89152700 90161500 90986000 91063115 91489840 91800800 91895860 92718808 92935700 93865057 93879500 94296125 94625440 94738000 95586400 96653128 96768100 97097000 98067970 98527520 99642400 100084600 100638824 100980880 101085446 101101000 101888800 104087984 104211800 105023840 105145040 107767000 108380272 108983875 109833100 110931431 111440875 112077680 114362300 114751000 114869825 115526224 115898510 116169625 118281800 119464618 119483000 120699040 120816410 120960125 123013072 123159400 124553000 125105750 125798530 126226100 127361000 127488361 128085776 130109980 130264750 131279800 131431300 132455440 134134000 135475340 136530992 137158000 137291375 139499360 140097100 142644320 142952875 142978000 144258400 144407780 145700984 147033376 147852250 148697120 148874000 150207200 150873800 153766340 153949250 154828960 156908752 157782625 158522000 160107220 162637475 164099750 164289125 165569300 168974000 169142974 169344175 170663740 174374200 175121375 175732960 175942000 176117942 178305400 180323000 180509725 181972000 182126230 182979680 183791720 185437616 185871400 187730114 187759000 188592250 189476000 192207925 193306256 193536200 194194000 196135940 200134025 200169200 201277648 201961760 202170892 202202000 206961625 208175968 208423600 210290080 213329675 215534000 216760544 217967750 219666200 221862862 222881750 224155360 228724600 229502000 229739650 231052448 231797020 232339250 236563600 238929236 238966000 241632820 241920250 245169925 246026144 246318800 249106000 250211500 251597060 252452200 252713615 254722000 254976722 256171552 260219960 260529500 262559600 262862600 264910880 268268000 270950680 273061984 274316000 274582750 280194200 285905750 285956000 288815560 289746275 291401968 295704500 297748000 298661545 301747600 302041025 307532680 307898500 313817504 314496325 315565250 317044000 320214440 325274950 328199500 328578250 331138600 337948000 338285948 338688350 341327480 348748400 350242750 351884000 352235884 356610800 360646000 361019450 364252460 367583440 370875232 371742800 375460228 375518000 377184500 384415850 386612512 387072400 388388000 392271880 400268050 400338400 402555296 404341784 404404000 413923250 416847200 422857435 426659350 431068000 435935500 439332400 440294855 443725724 445763500 455315575 457449200 459004000 459479300 463594040 464678500 469325285 473127200 477858472 477932000 483265640 483840500 490339850 492637600 498212000 500423000 503194120 504904400 505427230 509444000 509953444 520439920 521059000 525119200 525725200 541901360 549165500 554657155 560388400 571811500 574349125 577631120 579492550 582803936 591409000 597323090 603495200 604082050 615065360 615797000 628992650 631130500 637441805 640428880 650549900 656399000 657055399 657156500 662277200 676571896 677376700 682654960 697496800 700485500 704471768 713221600 721292000 722038900 728504920 735166880 743485600 750920456 751036000 754369000 768831700 774144800 776520017 784543760 800536100 808683568 813187375 827846500 845714870 846720875 853318700 871871000 878664800 880589710 887451448 891527000 902548625 910631150 914898400 918958600 927188080 929357000 938650570 955716944 961039625 966531280 967681000 980679700 1000670125 1000846000 1006388240 1009808800 1010854460 1019906888 1040879840 1042118000 1051450400 1066648375 1083802720 1098331000 1109314310 1120776800 1143623000 1148698250 1155262240 1158985100 1182818000 1194646180 1208164100 1220245741 1225849625 1230130720 1231594000 1257985300 1262261000 1263568075 1274883610 1280857760 1301099800 1312798000 1314110798 1314313000 1324554400 1353143792 1354753400 1365309920 1400971000 1408943536 1444077800 1448731375 1457009840 1493307725 1501840912 1508738000 1510205125 1537663400 1553040034 1569087520 1572481625 1601072200 1617367136 1626374750 1655693000 1691429740 1693441750 1706637400 1743742000 1761179420 1774902896 1783054000 1805097250 1821262300 1837917200 1854376160 1858714000 1877301140 1911433888 1922079250 1933062560 1935362000 1961359400 2001340250 2001692000 2012776480 2021708920 2039813776 2084236000 2114287175 2133296750 2196662000 2201474275 2218628620 2276577875 2287246000 2297396500 2317970200 2346626425 2365636000 2389292360 2416328200 2440491482 2451699250 2463188000 2515970600 2524522000 2527136150 2549767220 2602199600 2625596000 2628221596 2628626000 2706287584 2709506800 2773285775 2801942000 2817887072 2888155600 2897462750 2914019680 2986615450 3003681824 3017476000 3020410250 3075326800 3106080068 3144963250 3187209025 3202144400 3252749500 3285276995 3311386000 3382859480 3386883500 3413274800 3487484000 3522358840 3549805792 3566108000 3610194500 3642524600 3675834400 3717428000 3754602280 3844158500 3870724000 3882600085 3922718800 4002680500 4043417840 4079627552 4228574350 4266593500 4393324000 4402948550 4437257240 4553155750 4574492000 4594793000 4635940400 4693252850 4778584720 4832656400 4880982964 4903398500 5031941200 5049044000 5054272300 5099534440 5204399200 5256443192 5257252000 5419013600 5546571550 5603884000 5776311200 5794925500 5973230900 6040820500 6101228705 6150653600 6212160136 6289926500 6317840375 6374418050 6404288800 6505499000 6570553990 6622772000 6765718960 6773767000 6826549600 7044717680 7220389000 7285049200 7466538625 7509204560 7688317000 7765200170 7845437600 8005361000 8086835680 8457148700 8533187000 8541720187 8805897100 8874514480 9106311500 9189586000 9271880800 9386505700 9557169440 9665312800 9761965928 9806797000 10063882400 10108544600 10199068880 10512886384 10571435875 11007371375 11093143100 11589851000 11733132125 11946461800 12081641000 12202457410 12424320272 12579853000 12635680750 12748836100 13010998000 13141107980 13531437920 13547534000 13866428875 14089435360 14440778000 14570098400 14933077250 15018409120 15376634000 15530400340 15936045125 16010722000 16426384975 16914297400 17066374000 17083440374 17611794200 17749028960 18212623000 18379172000 18773011400 19413000425 19523931856 19613594000 20217089200 20398137760 21025772768 21142871750 22014742750 22186286200 23179702000 23466264250 23892923600 24163282000 24404914820 24848640544 25159706000 25271361500 25497672200 26021996000 26282215960 27095068000 27732857750 28881556000 29866154500 30506143525 30753268000 31060800680 31872090250 32021444000 32852769950 33828594800 34132748000 34166880748 35223588400 36425246000 37546022800 38826000850 39047863712 39227188000 40434178400 42285743500 42708600935 44029485500 44372572400 46359404000 46932528500 47785847200 48326564000 48809829640 50319412000 50542723000 50995344400 52564431920 55465715500 59732309000 61012287050 62121601360 63744180500 65705539900 67657189600 68333761496 70447176800 72850492000 75092045600 77652001700 82131924875 84571487000 85417201870 88058971000 88745144800 93865057000 97065002125 97619659280 101085446000 101990688800 105128863840 110931431000 119464618000 122024574100 124243202720 127488361000 131411079800 136667522992 152530717625 155304003400 164263849750 169142974000 170834403740 176117942000 187730114000 194130004250 195239318560 202170892000 213543004675 221862862000 238929236000 244049148200 254976722000 262822159600 273335045984 305061435250 310608006800 328527699500 338285948000 341668807480 352235884000 375460228000 388260008500 427086009350 443725724000 488098296400 509953444000 525644319200 610122870500 621216013600 657055399000 683337614960 776520017000 854172018700 976196592800 1067715023375 1220245741000 1314110798000 1366675229920 1553040034000 1708344037400 2135430046750 2440491482000 2628221596000 3106080068000 3416688074800 4270860093500 4880982964000 6833376149600 8541720187000 17083440374000 34166880748000
- Sum of all divisors σ(n): 117360683661312
- Sum of proper divisors (its aliquot sum) s(n): 83193802913312
- 34166880748000 is an abundant number, because the sum of its proper divisors (83193802913312) is greater than itself. Its abundance is 49026922165312
Bases of 34166880748000
- Binary: 1111100010011000110001100101001000001111000002
- Hexadecimal: 0x1F1318CA41E0
- Base-36: C401QMUHS
Squares and roots of 34166880748000
- 34166880748000 squared (341668807480002) is 1167375740048053039504000000
- 34166880748000 cubed (341668807480003) is 39885587698330075990312101068992000000000
-
The
square root of 34166880748000 is 5845244.2847155671 -
The
cube root of 34166880748000 is 32449.0343588059
Scales and comparisons
How big is 34166880748000?- 34,166,880,748,000 seconds is equal to 1,086,401 years, 6 weeks, 2 days, 15 hours, 46 minutes, 40 seconds.
-
To count from 1 to 34,166,880,748,000 would take you about two million, seven hundred sixteen thousand and 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 34166880748000 cubic inches would be around 2704.1 feet tall.
Recreational maths with 34166880748000
- 34166880748000 backwards is 00084708866143
- 34166880748000 is a
Harshad number . - The number of decimal digits it has is: 14
- The sum of 34166880748000's digits is 55
- 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 34166880748000 - Facts about the integer". Numbermatics.com. 2024. Web. 19 June 2024.
APA style:
Numbermatics. (2024). Number 34166880748000 - Facts about the integer. Retrieved 19 June 2024, from https://numbermatics.com/n/34166880748000/
Chicago style:
Numbermatics. 2024. "Number 34166880748000 - Facts about the integer". https://numbermatics.com/n/34166880748000/
The information we have on file for 34166880748000 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 34166880748000, math, Factors of 34166880748000, curriculum, school, college, exams, university, Prime factorization of 34166880748000, STEM, science, technology, engineering, physics, economics, calculator, thirty-four trillion, one hundred sixty-six billion, eight hundred eighty million, seven hundred forty-eight thousand.