1041419193750000
1,041,419,193,750,000 is an even composite number composed of five prime numbers multiplied together.
1041419193750000 is an even composite number. It is composed of five distinct prime numbers multiplied together. It has a total of two thousand, one hundred sixty divisors.
Prime factorization of 1041419193750000:
24 × 33 × 58 × 133 × 532
(2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 13 × 13 × 13 × 53 × 53)See below for interesting mathematical facts about the number 1041419193750000 from the Numbermatics database.
Names of 1041419193750000
- Cardinal: 1041419193750000 can be written as One quadrillion, forty-one trillion, four hundred nineteen billion, one hundred ninety-three million, seven hundred fifty thousand.
Scientific notation
- Scientific notation: 1.04141919375 × 1015
Factors of 1041419193750000
Divisors of 1041419193750000
- Number of divisors d(n): 2160
-
Complete list of divisors:
1 2 3 4 5 6 8 9 10 12 13 15 16 18 20 24 25 26 27 30 36 39 40 45 48 50 52 53 54 60 65 72 75 78 80 90 100 104 106 108 117 120 125 130 135 144 150 156 159 169 180 195 200 208 212 216 225 234 240 250 260 265 270 300 312 318 325 338 351 360 375 390 400 424 432 450 468 477 500 507 520 530 540 585 600 624 625 636 650 675 676 689 702 720 750 780 795 845 848 900 936 954 975 1000 1014 1040 1060 1080 1125 1170 1200 1250 1272 1300 1325 1350 1352 1378 1404 1431 1500 1521 1560 1590 1625 1690 1755 1800 1872 1875 1908 1950 2000 2028 2067 2120 2160 2197 2250 2340 2385 2500 2535 2544 2600 2650 2700 2704 2756 2808 2809 2862 2925 3000 3042 3120 3125 3180 3250 3375 3380 3445 3510 3600 3750 3816 3900 3975 4056 4134 4225 4240 4394 4500 4563 4680 4770 4875 5000 5070 5200 5300 5400 5512 5616 5618 5625 5724 5850 6000 6084 6201 6250 6360 6500 6591 6625 6750 6760 6890 7020 7155 7500 7605 7632 7800 7950 8112 8125 8268 8427 8450 8775 8788 8957 9000 9126 9360 9375 9540 9750 10000 10140 10335 10600 10800 10985 11024 11236 11250 11448 11700 11925 12168 12402 12500 12675 12720 13000 13182 13250 13500 13520 13780 14040 14045 14310 14625 15000 15210 15600 15625 15900 16250 16536 16854 16875 16900 17225 17550 17576 17914 18000 18252 18603 18750 19080 19500 19773 19875 20280 20670 21125 21200 21970 22472 22500 22815 22896 23400 23850 24336 24375 24804 25000 25281 25350 26000 26364 26500 26871 27000 27560 28080 28090 28125 28620 29250 30000 30420 31005 31250 31800 32500 32955 33072 33125 33708 33750 33800 34450 35100 35152 35775 35828 36504 36517 37206 37500 38025 38160 39000 39546 39750 40560 40625 41340 42135 42250 43875 43940 44785 44944 45000 45630 46800 46875 47700 48750 49608 50000 50562 50700 51675 52728 53000 53742 54000 54925 55120 56180 56250 57240 58500 59319 59625 60840 62010 62500 63375 63600 65000 65910 66250 67416 67500 67600 68900 70200 70225 71550 71656 73008 73034 73125 74412 75000 75843 76050 78000 78125 79092 79500 80613 81250 82680 84270 84375 84500 86125 87750 87880 89570 90000 91260 93015 93750 95400 97500 98865 99216 99375 101124 101400 103350 105456 105625 106000 107484 109551 109850 112360 112500 114075 114480 116441 117000 118638 119250 121680 121875 124020 125000 126405 126750 130000 131820 132500 134355 134832 135000 137800 140400 140450 140625 143100 143312 146068 146250 148824 150000 151686 152100 155025 156250 158184 159000 161226 162500 164775 165360 165625 168540 168750 169000 172250 175500 175760 178875 179140 182520 182585 186030 187500 190125 190800 195000 197730 198750 202248 202800 203125 206700 210675 211250 214968 219102 219375 219700 223925 224720 225000 228150 232882 234000 234375 237276 238500 241839 243750 248040 250000 252810 253500 258375 263640 265000 268710 270000 274625 275600 280900 281250 286200 292136 292500 296595 297648 298125 303372 304200 310050 312500 316368 316875 318000 322452 325000 328653 329550 331250 337080 337500 338000 344500 349323 351000 351125 357750 358280 365040 365170 365625 372060 375000 379215 380250 390000 390625 395460 397500 403065 404496 406250 413400 421350 421875 422500 429936 430625 438204 438750 439400 447850 450000 456300 465075 465764 468750 474552 474721 477000 483678 487500 494325 496080 496875 505620 507000 516750 527280 528125 530000 537420 547755 549250 561800 562500 570375 572400 582205 584272 585000 593190 596250 606744 608400 609375 620100 625000 632025 633750 644904 650000 657306 659100 662500 671775 674160 675000 689000 698646 702000 702250 703125 715500 716560 730340 731250 744120 750000 758430 760500 775125 781250 790920 795000 806130 812500 823875 826800 828125 842700 843750 845000 861250 876408 877500 878800 894375 895700 912600 912925 930150 931528 937500 949104 949442 950625 954000 967356 975000 985959 988650 993750 1011240 1014000 1015625 1033500 1047969 1053375 1056250 1074840 1095510 1096875 1098500 1119625 1123600 1125000 1140750 1164410 1170000 1171875 1186380 1192500 1209195 1213488 1218750 1240200 1250000 1264050 1267500 1289808 1291875 1314612 1318200 1325000 1343550 1350000 1373125 1378000 1397292 1404500 1406250 1424163 1431000 1460680 1462500 1482975 1488240 1490625 1516860 1521000 1550250 1562500 1581840 1584375 1590000 1612260 1625000 1643265 1647750 1656250 1685400 1687500 1690000 1722500 1746615 1752816 1755000 1755625 1788750 1791400 1825200 1825850 1828125 1860300 1863056 1875000 1896075 1898884 1901250 1934712 1950000 1971918 1977300 1987500 2015325 2022480 2031250 2067000 2095938 2106750 2109375 2112500 2149680 2153125 2191020 2193750 2197000 2239250 2250000 2281500 2325375 2328820 2343750 2372760 2373605 2385000 2418390 2437500 2471625 2480400 2484375 2528100 2535000 2583750 2629224 2636400 2640625 2650000 2687100 2738775 2746250 2794584 2809000 2812500 2848326 2851875 2862000 2911025 2921360 2925000 2965950 2981250 3033720 3042000 3046875 3100500 3125000 3143907 3160125 3168750 3224520 3250000 3286530 3295500 3312500 3358875 3370800 3375000 3445000 3493230 3510000 3511250 3515625 3577500 3582800 3651700 3656250 3720600 3750000 3792150 3797768 3802500 3869424 3875625 3943836 3954600 3975000 4030650 4062500 4119375 4134000 4140625 4191876 4213500 4218750 4225000 4272489 4306250 4382040 4387500 4394000 4471875 4478500 4563000 4564625 4650750 4657640 4687500 4745520 4747210 4753125 4770000 4836780 4875000 4929795 4943250 4968750 5056200 5070000 5078125 5167500 5239845 5258448 5266875 5281250 5374200 5477550 5484375 5492500 5589168 5598125 5618000 5625000 5696652 5703750 5822050 5850000 5931900 5962500 6045975 6067440 6093750 6171373 6201000 6250000 6287814 6320250 6337500 6449040 6459375 6573060 6591000 6625000 6717750 6750000 6865625 6890000 6986460 7022500 7031250 7120815 7155000 7303400 7312500 7414875 7441200 7453125 7584300 7595536 7605000 7751250 7887672 7909200 7921875 7950000 8061300 8125000 8216325 8238750 8281250 8383752 8427000 8437500 8450000 8544978 8612500 8733075 8764080 8775000 8778125 8943750 8957000 9126000 9129250 9140625 9301500 9315280 9375000 9480375 9494420 9506250 9673560 9750000 9859590 9886500 9937500 10076625 10112400 10156250 10335000 10479690 10533750 10546875 10562500 10748400 10765625 10955100 10968750 10985000 11196250 11250000 11393304 11407500 11626875 11644100 11863800 11868025 11925000 12091950 12187500 12342746 12358125 12402000 12421875 12575628 12640500 12675000 12817467 12918750 13146120 13182000 13203125 13250000 13435500 13693875 13731250 13972920 14045000 14062500 14241630 14259375 14310000 14555125 14606800 14625000 14829750 14906250 15168600 15210000 15234375 15502500 15719535 15775344 15800625 15843750 16122600 16250000 16432650 16477500 16562500 16767504 16794375 16854000 16875000 17089956 17225000 17466150 17550000 17556250 17887500 17914000 18258500 18281250 18514119 18603000 18750000 18960750 18988840 19012500 19347120 19378125 19719180 19773000 19875000 20153250 20312500 20596875 20670000 20703125 20959380 21067500 21093750 21125000 21362445 21531250 21910200 21937500 21970000 22359375 22392500 22786608 22815000 22823125 23253750 23288200 23727600 23736050 23765625 23850000 24183900 24375000 24648975 24685492 24716250 24843750 25151256 25281000 25350000 25634934 25837500 26199225 26292240 26334375 26406250 26871000 27387750 27421875 27462500 27945840 27990625 28090000 28125000 28483260 28518750 29110250 29250000 29659500 29812500 30229875 30337200 30468750 30856865 31005000 31439070 31601250 31687500 32245200 32296875 32865300 32955000 33125000 33588750 33750000 34179912 34328125 34450000 34932300 35112500 35604075 35775000 36517000 36562500 37028238 37074375 37206000 37265625 37921500 37977680 38025000 38756250 39438360 39546000 39609375 39750000 40306500 40625000 41081625 41193750 41406250 41918760 42135000 42187500 42250000 42724890 43062500 43665375 43820400 43875000 43890625 44718750 44785000 45630000 45646250 45703125 46507500 46576400 47401875 47472100 47531250 48367800 48750000 49297950 49370984 49432500 49687500 50302512 50383125 50562000 51269868 51675000 52398450 52668750 52812500 53742000 53828125 54775500 54843750 54925000 55542357 55981250 56250000 56966520 57037500 58134375 58220500 59319000 59340125 59625000 60459750 60937500 61713730 61790625 62010000 62109375 62878140 63202500 63375000 64087335 64593750 65730600 65910000 66015625 66250000 67177500 68359824 68469375 68656250 69864600 70225000 71208150 71296875 71550000 72775625 73034000 73125000 74056476 74148750 74531250 75843000 76050000 77512500 78597675 78876720 79003125 79218750 80613000 81250000 82163250 82387500 82812500 83837520 83971875 84270000 84375000 85449780 86125000 87330750 87750000 87781250 89437500 89570000 91292500 91406250 92570595 93015000 94803750 94944200 95062500 96735600 96890625 98595900 98741968 98865000 99375000 100766250 102539736 102984375 103350000 104796900 105337500 105625000 106812225 107656250 109551000 109687500 109850000 111084714 111796875 111962500 113933040 114075000 114115625 116268750 116441000 118638000 118680250 118828125 119250000 120919500 121875000 123244875 123427460 123581250 124218750 125756280 126405000 126750000 128174670 129187500 130996125 131461200 131671875 132031250 134355000 136938750 137109375 137312500 139729200 139953125 140450000 142416300 142593750 145551250 146250000 148112952 148297500 149062500 151149375 151686000 154284325 155025000 157195350 158006250 158437500 161226000 161484375 164326500 164775000 165625000 166627071 167943750 168750000 170899560 171640625 172250000 174661500 175562500 178020375 178875000 182585000 182812500 185141190 185371875 186030000 186328125 189607500 189888400 190125000 193781250 197191800 197730000 198046875 198750000 201532500 205079472 205408125 205968750 209593800 210675000 211250000 213624450 215312500 218326875 219102000 219375000 219453125 222169428 223593750 223925000 228150000 228231250 232537500 232882000 237009375 237360500 237656250 241839000 243750000 246489750 246854920 247162500 248437500 251512560 251915625 252810000 256349340 258375000 261992250 263343750 264062500 268710000 269140625 273877500 274218750 274625000 277711785 279906250 284832600 285187500 290671875 291102500 296225904 296595000 296700625 298125000 302298750 308568650 308953125 310050000 314390700 316012500 316875000 320436675 322968750 328653000 329550000 331250000 333254142 335887500 341799120 342346875 343281250 349323000 351125000 356040750 356484375 357750000 363878125 365170000 365625000 370282380 370743750 372656250 379215000 380250000 387562500 392988375 394383600 395015625 396093750 403065000 410816250 411937500 419187600 419859375 421350000 427248900 430625000 436653750 438750000 438906250 444338856 447187500 447850000 456462500 462852975 465075000 474018750 474721000 475312500 483678000 484453125 492979500 493709840 494325000 496875000 503831250 512698680 514921875 516750000 523984500 526687500 528125000 534061125 538281250 547755000 548437500 549250000 555423570 558984375 559812500 569665200 570375000 570578125 581343750 582205000 593190000 593401250 594140625 596250000 604597500 616224375 617137300 617906250 628781400 632025000 633750000 640873350 645937500 654980625 657306000 658359375 666508284 671775000 684693750 686562500 698646000 699765625 702250000 712081500 712968750 727756250 731250000 740564760 741487500 745312500 755746875 758430000 771421625 775125000 785976750 790031250 792187500 806130000 807421875 821632500 823875000 833135355 839718750 854497800 858203125 861250000 873307500 877812500 888677712 890101875 894375000 912925000 925705950 926859375 930150000 948037500 949442000 950625000 968906250 985959000 988650000 993750000 1007662500 1025397360 1027040625 1029843750 1047969000 1053375000 1056250000 1068122250 1076562500 1091634375 1095510000 1096875000 1097265625 1110847140 1117968750 1119625000 1140750000 1141156250 1162687500 1164410000 1185046875 1186802500 1188281250 1209195000 1232448750 1234274600 1235812500 1257562800 1259578125 1264050000 1281746700 1291875000 1309961250 1316718750 1333016568 1343550000 1369387500 1373125000 1388558925 1399531250 1424163000 1425937500 1453359375 1455512500 1481129520 1482975000 1483503125 1490625000 1511493750 1542843250 1544765625 1550250000 1571953500 1580062500 1584375000 1602183375 1614843750 1643265000 1647750000 1666270710 1679437500 1708995600 1711734375 1716406250 1746615000 1755625000 1780203750 1782421875 1788750000 1819390625 1825850000 1851411900 1853718750 1896075000 1901250000 1937812500 1964941875 1971918000 1975078125 2015325000 2054081250 2059687500 2095938000 2099296875 2106750000 2136244500 2153125000 2183268750 2193750000 2194531250 2221694280 2235937500 2239250000 2282312500 2314264875 2325375000 2370093750 2373605000 2376562500 2418390000 2422265625 2464897500 2468549200 2471625000 2519156250 2563493400 2574609375 2583750000 2619922500 2633437500 2666033136 2670305625 2738775000 2746250000 2777117850 2799062500 2848326000 2851875000 2852890625 2906718750 2911025000 2965950000 2967006250 2981250000 3022987500 3081121875 3085686500 3089531250 3143907000 3160125000 3168750000 3204366750 3229687500 3274903125 3286530000 3291796875 3332541420 3358875000 3423468750 3432812500 3493230000 3498828125 3511250000 3560407500 3564843750 3638781250 3702823800 3707437500 3778734375 3792150000 3857108125 3875625000 3929883750 3950156250 4030650000 4108162500 4119375000 4165676775 4198593750 4272489000 4306250000 4366537500 4389062500 4443388560 4450509375 4471875000 4564625000 4628529750 4634296875 4650750000 4740187500 4747210000 4753125000 4844531250 4929795000 4943250000 5038312500 5126986800 5135203125 5149218750 5239845000 5266875000 5340611250 5458171875 5477550000 5554235700 5598125000 5703750000 5705781250 5813437500 5822050000 5925234375 5934012500 6045975000 6162243750 6171373000 6179062500 6287814000 6297890625 6320250000 6408733500 6459375000 6549806250 6583593750 6665082840 6717750000 6846937500 6865625000 6942794625 6997656250 7120815000 7129687500 7266796875 7277562500 7405647600 7414875000 7417515625 7557468750 7714216250 7723828125 7751250000 7859767500 7900312500 8010916875 8216325000 8238750000 8331353550 8397187500 8544978000 8558671875 8733075000 8778125000 8901018750 8943750000 9096953125 9129250000 9257059500 9268593750 9480375000 9506250000 9689062500 9824709375 9859590000 9875390625 10076625000 10270406250 10298437500 10479690000 10496484375 10533750000 10681222500 10916343750 11108471400 11196250000 11411562500 11571324375 11626875000 11850468750 11868025000 12091950000 12324487500 12342746000 12358125000 12595781250 12817467000 12918750000 13099612500 13167187500 13330165680 13351528125 13693875000 13731250000 13885589250 13995312500 14241630000 14259375000 14264453125 14533593750 14555125000 14829750000 14835031250 15114937500 15405609375 15428432500 15447656250 15719535000 15800625000 16021833750 16374515625 16432650000 16662707100 16794375000 17117343750 17466150000 17556250000 17802037500 18193906250 18514119000 18537187500 18893671875 18960750000 19285540625 19378125000 19649418750 19750781250 20153250000 20540812500 20596875000 20828383875 20992968750 21362445000 21832687500 22216942800 22252546875 22823125000 23142648750 23171484375 23253750000 23700937500 23736050000 24648975000 24716250000 25191562500 25634934000 25676015625 26199225000 26334375000 26703056250 27290859375 27387750000 27771178500 27990625000 28518750000 28528906250 29067187500 29110250000 29626171875 29670062500 30229875000 30811218750 30856865000 30895312500 31439070000 31489453125 31601250000 32043667500 32749031250 33325414200 33588750000 34234687500 34713973125 35604075000 36387812500 37028238000 37074375000 37087578125 37787343750 38571081250 38756250000 39298837500 39501562500 40054584375 41081625000 41193750000 41656767750 41985937500 42724890000 42793359375 43665375000 44505093750 45484765625 45646250000 46285297500 46342968750 47401875000 49123546875 49297950000 50383125000 51352031250 52398450000 52668750000 53406112500 54581718750 55542357000 55981250000 57057812500 57856621875 58134375000 59252343750 59340125000 60459750000 61622437500 61713730000 61790625000 62978906250 64087335000 65498062500 66650828400 66757640625 68469375000 69427946250 71208150000 72775625000 74148750000 74175156250 75574687500 77028046875 77142162500 78597675000 79003125000 80109168750 81872578125 82163250000 83313535500 83971875000 85586718750 87330750000 89010187500 90969531250 92570595000 92685937500 94468359375 94803750000 96427703125 98247093750 100766250000 102704062500 104141919375 106812225000 109163437500 111084714000 111262734375 114115625000 115713243750 116268750000 118504687500 118680250000 123244875000 123581250000 125957812500 128174670000 128380078125 130996125000 133515281250 136454296875 136938750000 138855892500 145551250000 148350312500 151149375000 154056093750 154284325000 157195350000 158006250000 160218337500 163745156250 166627071000 167943750000 171173437500 173569865625 178020375000 181939062500 185141190000 185371875000 185437890625 188936718750 192855406250 196494187500 200272921875 205408125000 208283838750 213624450000 218326875000 222525468750 228231250000 231426487500 237009375000 245617734375 246489750000 251915625000 256760156250 261992250000 267030562500 272908593750 277711785000 289283109375 296700625000 302298750000 308112187500 308568650000 320436675000 327490312500 333254142000 333788203125 342346875000 347139731250 356040750000 363878125000 370743750000 370875781250 377873437500 385140234375 385710812500 392988375000 400545843750 409362890625 410816250000 416567677500 436653750000 445050937500 462852975000 474018750000 482138515625 491235468750 503831250000 513520312500 520709596875 534061125000 545817187500 555423570000 556313671875 578566218750 593401250000 616224375000 640873350000 654980625000 667576406250 684693750000 694279462500 727756250000 741751562500 755746875000 770280468750 771421625000 785976750000 801091687500 818725781250 833135355000 867849328125 890101875000 925705950000 964277031250 982470937500 1001364609375 1027040625000 1041419193750 1068122250000 1091634375000 1112627343750 1157132437500 1228088671875 1232448750000 1309961250000 1335152812500 1388558925000 1446415546875 1483503125000 1511493750000 1540560937500 1542843250000 1602183375000 1637451562500 1666270710000 1668941015625 1735698656250 1780203750000 1928554062500 1964941875000 2002729218750 2054081250000 2082838387500 2183268750000 2225254687500 2314264875000 2410692578125 2456177343750 2603547984375 2670305625000 2777117850000 2892831093750 2967006250000 3081121875000 3204366750000 3274903125000 3337882031250 3471397312500 3857108125000 3929883750000 4005458437500 4165676775000 4339246640625 4450509375000 4628529750000 4821385156250 4912354687500 5006823046875 5207095968750 5340611250000 5785662187500 6162243750000 6549806250000 6675764062500 6942794625000 7232077734375 7714216250000 8010916875000 8331353550000 8678493281250 8901018750000 9642770312500 9824709375000 10013646093750 10414191937500 11571324375000 13017739921875 13351528125000 13885589250000 14464155468750 16021833750000 17356986562500 19285540625000 19649418750000 20027292187500 20828383875000 21696233203125 23142648750000 26035479843750 26703056250000 28928310937500 34713973125000 38571081250000 40054584375000 41656767750000 43392466406250 52070959687500 57856621875000 65088699609375 69427946250000 80109168750000 86784932812500 104141919375000 115713243750000 130177399218750 173569865625000 208283838750000 260354798437500 347139731250000 520709596875000 1041419193750000
- Sum of all divisors σ(n): 4125625622053600
- Sum of proper divisors (its aliquot sum) s(n): 3084206428303600
- 1041419193750000 is an abundant number, because the sum of its proper divisors (3084206428303600) is greater than itself. Its abundance is 2042787234553600
Bases of 1041419193750000
- Binary: 111011001100101010010011010001101100010001111100002
- Hexadecimal: 0x3B32A4D1B11F0
- Base-36: A95HDFB8C0
Squares and roots of 1041419193750000
- 1041419193750000 squared (10414191937500002) is 1084553937110900039062500000000
- 1041419193750000 cubed (10414191937500003) is 1129475286764421723017312255859375000000000000
-
The
square root of 1041419193750000 is 32271027.1567237225 -
The
cube root of 1041419193750000 is 101362.0049956603
Scales and comparisons
How big is 1041419193750000?- 1,041,419,193,750,000 seconds is equal to 33,113,909 years, 2 weeks, 15 hours.
-
To count from 1 to 1,041,419,193,750,000 would take you about ninety-nine million, three hundred forty-one thousand, seven hundred twenty-seven 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 1041419193750000 cubic inches would be around 8446.8 feet tall.
Recreational maths with 1041419193750000
- 1041419193750000 backwards is 0000573919141401
- 1041419193750000 is a
Harshad number . - The number of decimal digits it has is: 16
- The sum of 1041419193750000's digits is 45
- 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 1041419193750000 - Facts about the integer". Numbermatics.com. 2024. Web. 9 May 2024.
APA style:
Numbermatics. (2024). Number 1041419193750000 - Facts about the integer. Retrieved 9 May 2024, from https://numbermatics.com/n/1041419193750000/
Chicago style:
Numbermatics. 2024. "Number 1041419193750000 - Facts about the integer". https://numbermatics.com/n/1041419193750000/
The information we have on file for 1041419193750000 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 1041419193750000, math, Factors of 1041419193750000, curriculum, school, college, exams, university, Prime factorization of 1041419193750000, STEM, science, technology, engineering, physics, economics, calculator, one quadrillion, forty-one trillion, four hundred nineteen billion, one hundred ninety-three million, seven hundred fifty thousand.