967184659650000
967,184,659,650,000 is an even composite number composed of six prime numbers multiplied together.
What does the number 967184659650000 look like?
This visualization shows the relationship between its 6 prime factors (large circles) and 2160 divisors.
967184659650000 is an even composite number. It is composed of six distinct prime numbers multiplied together. It has a total of two thousand, one hundred sixty divisors.
Prime factorization of 967184659650000:
24 × 3 × 55 × 113 × 312 × 712
(2 × 2 × 2 × 2 × 3 × 5 × 5 × 5 × 5 × 5 × 11 × 11 × 11 × 31 × 31 × 71 × 71)See below for interesting mathematical facts about the number 967184659650000 from the Numbermatics database.
Names of 967184659650000
- Cardinal: 967184659650000 can be written as Nine hundred sixty-seven trillion, one hundred eighty-four billion, six hundred fifty-nine million, six hundred fifty thousand.
Scientific notation
- Scientific notation: 9.6718465965 × 1014
Factors of 967184659650000
Divisors of 967184659650000
- Number of divisors d(n): 2160
-
Complete list of divisors:
1 2 3 4 5 6 8 10 11 12 15 16 20 22 24 25 30 31 33 40 44 48 50 55 60 62 66 71 75 80 88 93 100 110 120 121 124 125 132 142 150 155 165 176 186 200 213 220 240 242 248 250 264 275 284 300 310 330 341 355 363 372 375 400 426 440 465 484 496 500 528 550 568 600 605 620 625 660 682 710 726 744 750 775 781 825 852 880 930 961 968 1000 1023 1065 1100 1136 1200 1210 1240 1250 1320 1331 1364 1375 1420 1452 1488 1500 1550 1562 1650 1704 1705 1775 1815 1860 1875 1922 1936 2000 2046 2130 2200 2201 2325 2343 2420 2480 2500 2640 2662 2728 2750 2840 2883 2904 3000 3025 3100 3124 3125 3300 3408 3410 3550 3630 3720 3750 3751 3844 3875 3905 3993 4092 4125 4260 4400 4402 4650 4686 4805 4840 5000 5041 5115 5324 5325 5456 5500 5680 5766 5808 6000 6050 6200 6248 6250 6600 6603 6655 6820 6875 7100 7260 7440 7500 7502 7688 7750 7810 7986 8184 8250 8520 8525 8591 8804 8875 9075 9300 9372 9375 9610 9680 10000 10082 10230 10571 10648 10650 11000 11005 11253 11532 11625 11715 12100 12400 12496 12500 13200 13206 13310 13640 13750 14200 14415 14520 15000 15004 15123 15125 15376 15500 15620 15972 16368 16500 17040 17050 17182 17608 17750 18150 18600 18744 18750 18755 19220 19375 19525 19965 20164 20460 20625 21142 21296 21300 22000 22010 22506 23064 23250 23430 24025 24200 24211 25000 25205 25575 25773 26412 26620 26625 27280 27500 28400 28830 29040 30000 30008 30246 30250 31000 31240 31713 31944 33000 33015 33275 34100 34364 34375 35216 35500 36300 37200 37488 37500 37510 38440 38750 39050 39930 40328 40920 41250 41261 42284 42600 42625 42955 44020 44375 45012 45375 46128 46500 46860 48050 48400 48422 50000 50410 51150 51546 52824 52855 53240 53250 55000 55025 55451 56265 57660 58125 58575 60016 60492 60500 62000 62480 63426 63888 66000 66030 66550 68200 68231 68728 68750 71000 72075 72600 72633 75000 75020 75615 75625 76880 77500 78100 79860 80656 81840 82500 82522 84568 85200 85250 85910 88040 88750 90024 90750 93000 93720 93775 94501 96100 96844 96875 97625 99825 100820 102300 103092 103125 105648 105710 106480 106500 110000 110050 110902 112530 115320 116250 116281 117150 120125 120984 121000 121055 123783 126025 126852 127875 128865 132060 133100 133125 136400 136462 137456 137500 142000 144150 145200 145266 150000 150040 151230 151250 155000 156200 156271 158565 159720 165000 165044 165075 166353 166375 169136 170500 171820 176080 177500 180048 181500 186000 187440 187550 189002 192200 193688 193750 195250 199650 201640 204600 204693 206184 206250 206305 211420 213000 213125 214775 220100 221804 221875 225060 226875 230640 232500 232562 234300 240250 241968 242000 242110 247566 252050 253704 255750 257730 264120 264275 266200 266250 266321 272924 275000 275125 277255 281325 283503 288300 290532 290625 292875 300080 302460 302500 310000 312400 312542 317130 319440 330000 330088 330150 332706 332750 341000 341155 343640 348843 355000 360375 363000 363165 375100 378004 378075 378125 384400 387376 387500 390500 399300 403280 409200 409386 412368 412500 412610 422840 426000 426250 429550 440200 443608 443750 450120 453750 465000 465124 468600 468813 468875 472505 480500 484220 488125 495132 499125 504100 507408 511500 515460 528240 528550 532400 532500 532642 545848 550000 550250 554510 562650 567006 576600 581064 581250 581405 585750 600625 604920 605000 605275 609961 618915 625084 630125 634260 639375 644325 660176 660300 665412 665500 665625 682000 682310 687280 697686 710000 720750 726000 726330 750200 750541 756008 756150 756250 775000 781000 781355 792825 798600 798963 818772 825000 825220 825375 831765 831875 845680 852500 859100 880400 887216 887500 900240 907500 930000 930248 937200 937626 937750 945010 961000 968440 976250 990264 998250 1008200 1023000 1023465 1030920 1031525 1057100 1065000 1065284 1065625 1073875 1091696 1100500 1109020 1125300 1134012 1134375 1153200 1162128 1162500 1162810 1171500 1201250 1209840 1210000 1210550 1219922 1237830 1250168 1260250 1268520 1278750 1279091 1288650 1320600 1321375 1330824 1331000 1331250 1331605 1364620 1375625 1386275 1395372 1406625 1417515 1441500 1452660 1464375 1500400 1501082 1512016 1512300 1512500 1550000 1562000 1562710 1585650 1597200 1597926 1637544 1650000 1650440 1650750 1663530 1663750 1705000 1705775 1718200 1718981 1744215 1775000 1801875 1815000 1815825 1829883 1860496 1875252 1875500 1890020 1890375 1922000 1936880 1952500 1980528 1996500 2016400 2046000 2046930 2061840 2063050 2114200 2130000 2130568 2131250 2147750 2201000 2218040 2250600 2251623 2268024 2268750 2325000 2325620 2343000 2344065 2344375 2362525 2402500 2421100 2439844 2440625 2475660 2495625 2500336 2520500 2537040 2557500 2558182 2577300 2641200 2642750 2661648 2662000 2662500 2663210 2729240 2751250 2772550 2790744 2813250 2835030 2883000 2905320 2907025 2928750 2929531 3002164 3003125 3024600 3025000 3026375 3049805 3094575 3125420 3150625 3171300 3195852 3196875 3221625 3275088 3300880 3301500 3327060 3327500 3410000 3411550 3436400 3437962 3488430 3550000 3603750 3630000 3631650 3659766 3750504 3751000 3752705 3780040 3780750 3837273 3905000 3906775 3964125 3993000 3994815 4093860 4126100 4126875 4158825 4159375 4228400 4261136 4262500 4295500 4402000 4436080 4501200 4503246 4536048 4537500 4650000 4651240 4686000 4688130 4688750 4725050 4805000 4842200 4844401 4879688 4881250 4951320 4991250 5041000 5115000 5116364 5117325 5154600 5156943 5157625 5285500 5325000 5326420 5369375 5458480 5502500 5545100 5581488 5626500 5670060 5766000 5810640 5814050 5857500 5859062 6004328 6006250 6049200 6050000 6052750 6099610 6189150 6250840 6301250 6342600 6391704 6393750 6395455 6443250 6603000 6606875 6654120 6655000 6658025 6709571 6823100 6875924 6878125 6931375 6976860 7033125 7087575 7207500 7263300 7319532 7321875 7501008 7502000 7505410 7560080 7561500 7674546 7810000 7813550 7928250 7986000 7989630 8187720 8252200 8253750 8255951 8317650 8318750 8525000 8528875 8591000 8594905 8721075 8788593 9006492 9009375 9075000 9079125 9149415 9302480 9376260 9377500 9450100 9451875 9610000 9684400 9688802 9759376 9762500 9902640 9982500 10082000 10230000 10232728 10234650 10309200 10313886 10315250 10571000 10650000 10652840 10738750 11005000 11090200 11253000 11258115 11340120 11628100 11715000 11718124 11720325 11721875 11812625 12008656 12012500 12105500 12199220 12378300 12478125 12501680 12602500 12685200 12783408 12787500 12790910 12886500 13206000 13213750 13308240 13310000 13316050 13419142 13646200 13751848 13756250 13862750 13953720 14066250 14175150 14415000 14526600 14533203 14535125 14639064 14643750 14647655 15010820 15123000 15131875 15249025 15349092 15472875 15627100 15753125 15856500 15979260 16108125 16375440 16504400 16507500 16511902 16635300 16637500 17050000 17057750 17182000 17189810 17442150 17577186 18012984 18018750 18150000 18158250 18298830 18752520 18755000 18763525 18900200 18903750 18908791 19186365 19377604 19525000 19533875 19820625 19965000 19974075 20128713 20465456 20469300 20627772 20630500 20634375 20794125 21142000 21305680 21477500 22010000 22180400 22506000 22516230 22680240 23256200 23430000 23436248 23440650 23443750 23625250 24025000 24211000 24222005 24398440 24756600 24767853 24956250 25205000 25575000 25581820 25586625 25773000 25784715 25788125 26427500 26632100 26838284 26846875 27292400 27503696 27512500 27725500 27907440 28132500 28350300 28830000 29053200 29066406 29070250 29278128 29287500 29295310 30021640 30246000 30263750 30498050 30698184 30945750 31254200 31506250 31713000 31958520 31977275 32216250 33015000 33023804 33034375 33270600 33275000 33290125 33547855 34115500 34379620 34656875 34884300 35154372 35165625 35437875 36025968 36037500 36316500 36597660 37505040 37510000 37527050 37800400 37807500 37817582 38372730 38755208 39050000 39067750 39641250 39930000 39948150 40257426 40938600 41255544 41261000 41268750 41279755 41588250 42644375 42955000 42974525 43605375 43942965 45032460 45395625 45747075 46512400 46872496 46881300 46887500 47250500 47259375 48050000 48422000 48444010 48796880 49513200 49535706 49912500 50410000 51150000 51163640 51173250 51546000 51569430 51576250 52855000 53264200 53288411 53676568 53693750 55025000 55451000 56265000 56290575 56700600 56726373 58132812 58140500 58575000 58590620 58601625 59063125 60043280 60527500 60996100 61396368 61891500 62508400 63012500 63426000 63917040 63954550 64432500 66030000 66047608 66068750 66541200 66550000 66580250 67095710 68231000 68759240 69313750 69768600 70308744 70331250 70875750 72075000 72633000 72666015 72675625 73195320 73238275 75054100 75615000 75635164 75659375 76245125 76745460 77364375 77510416 78135500 79282500 79896300 80514852 80540625 81877200 82511088 82522000 82537500 82559510 83176500 85288750 85910000 85949050 87210750 87885930 90064920 90791250 90815461 91494150 93762600 93775000 93817625 94501000 94518750 94543955 95931825 96888020 97669375 99071412 99103125 99825000 99870375 100643565 102327280 102346500 103138860 103152500 103970625 105710000 106528400 106576822 107353136 107387500 110050000 110902000 112530000 112581150 113401200 113452746 116265624 116281000 117150000 117181240 117203250 118126250 121055000 121110025 121992200 123783000 123839265 126025000 127909100 127933125 128865000 128923575 128940625 132095216 132137500 133160500 134191420 136462000 137518480 138627500 139537200 140617488 140662500 141751500 144150000 145266000 145332030 145351250 146390640 146476550 150108200 151230000 151270328 151318750 152490250 153490920 154728750 156271000 158565000 159792600 159865233 159886375 161029704 161081250 165075000 165119020 166353000 166450625 167739275 170577500 171898100 173284375 174421500 175771860 177189375 180129840 181582500 181630922 182988300 187525200 187550000 187635250 189002000 189037500 189087910 191863650 193776040 195338750 198142824 198206250 199650000 199740750 201287130 204693000 206277720 206305000 206398775 207941250 207996701 213153644 213221875 214775000 214872625 218026875 219714825 225162300 226905492 226978125 228735375 232531248 232562000 234362480 234406500 236252500 242110000 242220050 243984400 247566000 247678530 252050000 255818200 255866250 257730000 257847150 257881250 264275000 266321000 266442055 268382840 272446383 277255000 281325000 281452875 283503000 283631865 290664060 290702500 292953100 293008125 295315625 300216400 302540656 302637500 304980500 306981840 309457500 312542000 317130000 319585200 319730466 319772750 322059408 322162500 330150000 330238040 332706000 332901250 335478550 341155000 343796200 346568750 348843000 351543720 354378750 363165000 363261844 363330075 363378125 365976600 366191375 375270500 378075000 378175820 381225625 383727300 386821875 387552080 390677500 396285648 396412500 399481500 402574260 409386000 412555440 412610000 412797550 415882500 415993402 426307288 426443750 429550000 429745250 436053750 439429650 450324600 453810984 453956250 454077305 457470750 468813000 469088125 472505000 472719775 479659125 484440100 488346875 495357060 499351875 503217825 511636400 511732500 515694300 515762500 519853125 528550000 532642000 532884110 536765680 544892766 554510000 562650000 562905750 567006000 567263730 581328120 581405000 585906200 586016250 586172521 590631250 605275000 605550125 609961000 618915000 619196325 623990103 639460932 639545500 639665625 644325000 644617875 660476080 665802500 670957100 682310000 687592400 693137500 697686000 703087440 708757500 726330000 726523688 726660150 726756250 731953200 732382750 750541000 756150000 756351640 762451250 767454600 773643750 781355000 792825000 798963000 799326165 799431875 805148520 825595100 831765000 831986804 832253125 838696375 852614576 852887500 859490500 872107500 878859300 885946875 900649200 907621968 907912500 908154610 914941500 937626000 938176250 945010000 945439550 959318250 968880200 976693750 990714120 998703750 1006435650 1023465000 1031388600 1031525000 1031993875 1039706250 1039983505 1065768220 1074363125 1089785532 1090134375 1098574125 1125811500 1134527460 1143676875 1162656240 1162810000 1171812400 1172032500 1172345042 1181262500 1210550000 1211100250 1219922000 1237830000 1238392650 1247980206 1278921864 1279091000 1279331250 1288650000 1289235750 1331605000 1332210275 1341914200 1362231915 1386275000 1407264375 1417515000 1418159325 1453047376 1453320300 1453512500 1464765500 1465040625 1501082000 1512703280 1524902500 1534909200 1547287500 1562710000 1585650000 1597926000 1598652330 1598863750 1610297040 1651190200 1663530000 1663973608 1664506250 1677392750 1705775000 1718981000 1744215000 1757718600 1758517563 1771893750 1815825000 1816309220 1816650375 1829883000 1830956875 1876352500 1890879100 1906128125 1918636500 1937760400 1953387500 1981428240 1997407500 2012871300 2046930000 2062777200 2063050000 2063987750 2079412500 2079967010 2131536440 2148726250 2179571064 2180268750 2197148250 2251623000 2269054920 2270386525 2287353750 2344065000 2344690084 2345440625 2362525000 2363598875 2398295625 2422200500 2476785300 2495960412 2496759375 2516089125 2557843728 2558182000 2558662500 2578471500 2663210000 2664420550 2683828400 2724463830 2772550000 2814528750 2835030000 2836318650 2906640600 2907025000 2929531000 2930081250 2930862605 3027750625 3049805000 3094575000 3095981625 3119950515 3197304660 3197727500 3223089375 3302380400 3327947216 3329012500 3354785500 3411550000 3437962000 3488430000 3515437200 3517035126 3543787500 3631650000 3632618440 3633300750 3659766000 3661913750 3752705000 3781758200 3812256250 3837273000 3906775000 3994815000 3996630825 3997159375 4025742600 4127975500 4158825000 4159934020 4193481875 4263072880 4297452500 4359142128 4360537500 4394296500 4503246000 4538109840 4540773050 4574707500 4688130000 4689380168 4690881250 4725050000 4727197750 4796591250 4844401000 4953570600 4991920824 4993518750 5032178250 5117325000 5156943000 5159969375 5199917525 5328841100 5371815625 5448927660 5492870625 5629057500 5672637300 5718384375 5813281200 5814050000 5859062000 5860162500 5861725210 6055501250 6099610000 6189150000 6191963250 6239901030 6394609320 6395455000 6446178750 6447897731 6658025000 6661051375 6709571000 6811159575 7034070252 7036321875 7087575000 7090796625 7265236880 7266601500 7323827500 7505410000 7563516400 7624512500 7674546000 7813550000 7989630000 7993261650 7994318750 8051485200 8255951000 8317650000 8319868040 8386963750 8594905000 8721075000 8788593000 8792587815 9081546100 9083251875 9149415000 9154784375 9378760336 9381762500 9454395500 9593182500 9688802000 9907141200 9983841648 9987037500 10064356500 10234650000 10313886000 10319938750 10399835050 10657682200 10743631250 10897855320 10985741250 11258115000 11345274600 11351932625 11436768750 11720325000 11723450420 11817994375 11991478125 12111002500 12383926500 12479802060 12580445625 12789218640 12790910000 12892357500 12895795462 13316050000 13322102750 13419142000 13622319150 14068140504 14072643750 14175150000 14181593250 14533203000 14647655000 14654313025 15138753125 15249025000 15479908125 15599752575 15986523300 15988637500 16115446875 16511902000 16639736080 16773927500 17189810000 17442150000 17577186000 17585175630 18163092200 18166503750 18298830000 18309568750 18763525000 18908791000 19186365000 19343693193 19974075000 19983154125 20128713000 20639877500 20799670100 20967409375 21315364400 21487262500 21795710640 21971482500 22516230000 22690549200 22703865250 22873537500 23440650000 23446900840 23635988750 23982956250 24222005000 24767853000 24959604120 25160891250 25784715000 25791590924 25799846875 25999587625 26644205500 27244638300 27464353125 28136281008 28145287500 28363186500 29066406000 29295310000 29308626050 30277506250 30498050000 30959816250 31199505150 31973046600 31977275000 32230893750 32239488655 33305256875 33547855000 34055797875 35170351260 35453983125 36326184400 36333007500 36619137500 37527050000 37817582000 38372730000 38687386386 39948150000 39966308250 40257426000 41279755000 41599340200 41934818750 42974525000 43942965000 43962939075 45407730500 45416259375 45747075000 46893801680 47271977500 47965912500 48444010000 49535706000 49919208240 50321782500 51569430000 51583181848 51599693750 51999175250 53288411000 54489276600 54928706250 56290575000 56726373000 56759663125 58617252100 59089971875 60555012500 61919632500 62399010300 62902228125 63946093200 63954550000 64461787500 64478977310 66610513750 67095710000 68111595750 70340702520 70907966250 72666015000 73238275000 73271565125 77374772772 77399540625 77998762875 79932616500 82559510000 83198680400 83869637500 85949050000 87885930000 87925878150 90815461000 90832518750 91494150000 94543955000 95931825000 96718465965 99915770625 100643565000 103166363696 103199387500 103998350500 106576822000 108978553200 109857412500 112581150000 113452746000 113519326250 117234504200 118179943750 121110025000 123839265000 124798020600 125804456250 128923575000 128957954620 129997938125 133221027500 136223191500 140681405040 141815932500 145332030000 146476550000 146543130250 154749545544 154799081250 155997525750 159865233000 161197443275 166526284375 167739275000 170278989375 175851756300 177269915625 181630922000 181665037500 189087910000 191863650000 193436931930 199831541250 201287130000 206398775000 207996701000 219714825000 219814695375 227038652500 234469008400 236359887500 242220050000 247678530000 249596041200 251608912500 257847150000 257915909240 259995876250 266442055000 272446383000 283631865000 283798315625 293086260500 309499091088 309598162500 311995051500 319730466000 322394886550 333052568750 335478550000 340557978750 351703512600 354539831250 363330075000 366357825625 386873863860 389993814375 399663082500 412797550000 415993402000 439429650000 439629390750 454077305000 472719775000 483592329825 499578853125 503217825000 515831818480 519991752500 532884110000 544892766000 567263730000 567596631250 586172521000 619196325000 623990103000 644789773100 649989690625 666105137500 681115957500 703407025200 709079662500 726660150000 732715651250 773747727720 779987628750 799326165000 805987216375 851394946875 879258781500 908154610000 945439550000 967184659650 999157706250 1006435650000 1039983505000 1099073476875 1135193262500 1172345042000 1238392650000 1247980206000 1289579546200 1299979381250 1332210275000 1362231915000 1418159325000 1465431302500 1547495455440 1559975257500 1598652330000 1611974432750 1702789893750 1758517563000 1831789128125 1934369319300 1949969071875 1998315412500 2079967010000 2198146953750 2270386525000 2417961649125 2579159092400 2599958762500 2664420550000 2724463830000 2836318650000 2930862605000 3119950515000 3223948865500 3405579787500 3517035126000 3663578256250 3868738638600 3899938143750 3996630825000 4029936081875 4396293907500 4540773050000 4835923298250 5199917525000 5495367384375 5861725210000 6239901030000 6447897731000 6811159575000 7327156512500 7737477277200 7799876287500 7993261650000 8059872163750 8792587815000 9671846596500 10399835050000 10990734768750 12089808245625 12895795462000 13622319150000 14654313025000 15599752575000 16119744327500 17585175630000 19343693193000 20149680409375 21981469537500 24179616491250 29308626050000 31199505150000 32239488655000 38687386386000 40299360818750 43962939075000 48359232982500 60449041228125 64478977310000 80598721637500 87925878150000 96718465965000 120898082456250 161197443275000 193436931930000 241796164912500 322394886550000 483592329825000 967184659650000
- Sum of all divisors σ(n): 3600145408071744
- Sum of proper divisors (its aliquot sum) s(n): 2632960748421744
- 967184659650000 is an abundant number, because the sum of its proper divisors (2632960748421744) is greater than itself. Its abundance is 1665776088771744
Bases of 967184659650000
- Binary: 110110111110100110001110100001001000010101110100002
- Hexadecimal: 0x36FA63A1215D0
- Base-36: 9IU6HYDYHC
Squares and roots of 967184659650000
- 967184659650000 squared (9671846596500002) is 935446165862286338122500000000
- 967184659650000 cubed (9671846596500003) is 904749181550412860707854982507125000000000000
-
The
square root of 967184659650000 is 31099592.5962061439 -
The
cube root of 967184659650000 is 98893.9673398425
Scales and comparisons
How big is 967184659650000?- 967,184,659,650,000 seconds is equal to 30,753,480 years, 24 weeks, 6 days, 2 hours, 20 minutes.
-
To count from 1 to 967,184,659,650,000 would take you about seventy-six million, eight hundred eighty-three thousand, seven hundred one 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 967184659650000 cubic inches would be around 8241.2 feet tall.
Recreational maths with 967184659650000
- 967184659650000 backwards is 000056956481769
- 967184659650000 is a
Harshad number . - The number of decimal digits it has is: 15
- The sum of 967184659650000's digits is 66
- 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 967184659650000 - Facts about the integer". Numbermatics.com. 2024. Web. 7 June 2024.
APA style:
Numbermatics. (2024). Number 967184659650000 - Facts about the integer. Retrieved 7 June 2024, from https://numbermatics.com/n/967184659650000/
Chicago style:
Numbermatics. 2024. "Number 967184659650000 - Facts about the integer". https://numbermatics.com/n/967184659650000/
The information we have on file for 967184659650000 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 967184659650000, math, Factors of 967184659650000, curriculum, school, college, exams, university, Prime factorization of 967184659650000, STEM, science, technology, engineering, physics, economics, calculator, nine hundred sixty-seven trillion, one hundred eighty-four billion, six hundred fifty-nine million, six hundred fifty thousand.