968764129533900
968,764,129,533,900 is an even composite number composed of six prime numbers multiplied together.
What does the number 968764129533900 look like?
This visualization shows the relationship between its 6 prime factors (large circles) and 2160 divisors.
968764129533900 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 968764129533900:
22 × 34 × 52 × 73 × 17 × 295
(2 × 2 × 3 × 3 × 3 × 3 × 5 × 5 × 7 × 7 × 7 × 17 × 29 × 29 × 29 × 29 × 29)See below for interesting mathematical facts about the number 968764129533900 from the Numbermatics database.
Names of 968764129533900
- Cardinal: 968764129533900 can be written as Nine hundred sixty-eight trillion, seven hundred sixty-four billion, one hundred twenty-nine million, five hundred thirty-three thousand, nine hundred.
Scientific notation
- Scientific notation: 9.687641295339 × 1014
Factors of 968764129533900
Divisors of 968764129533900
- Number of divisors d(n): 2160
-
Complete list of divisors:
1 2 3 4 5 6 7 9 10 12 14 15 17 18 20 21 25 27 28 29 30 34 35 36 42 45 49 50 51 54 58 60 63 68 70 75 81 84 85 87 90 98 100 102 105 108 116 119 126 135 140 145 147 150 153 162 170 174 175 180 189 196 203 204 210 225 238 245 252 255 261 270 290 294 300 306 315 324 340 343 348 350 357 378 405 406 420 425 435 441 450 459 476 490 493 510 522 525 540 567 580 588 595 609 612 630 675 686 700 714 725 735 756 765 783 810 812 833 841 850 870 882 900 918 945 980 986 1015 1020 1029 1044 1050 1071 1134 1190 1218 1225 1260 1275 1305 1323 1350 1372 1377 1421 1428 1450 1470 1479 1530 1566 1575 1620 1666 1682 1700 1715 1740 1764 1785 1827 1836 1890 1972 2025 2030 2058 2100 2142 2175 2205 2268 2295 2349 2380 2436 2450 2465 2499 2523 2550 2610 2646 2700 2754 2835 2842 2900 2940 2958 2975 3045 3060 3087 3132 3150 3213 3332 3364 3430 3451 3570 3654 3675 3780 3825 3915 3969 4050 4060 4116 4165 4205 4263 4284 4350 4410 4437 4590 4698 4725 4900 4930 4998 5046 5075 5100 5145 5220 5292 5355 5481 5508 5670 5684 5831 5887 5916 5950 6090 6174 6300 6426 6525 6615 6860 6885 6902 7105 7140 7308 7350 7395 7497 7569 7650 7830 7938 8100 8330 8410 8526 8575 8700 8820 8874 8925 9135 9180 9261 9396 9450 9639 9860 9947 9996 10092 10150 10290 10353 10710 10962 11025 11340 11475 11662 11745 11774 11900 12180 12325 12348 12495 12615 12789 12852 13050 13230 13311 13770 13804 14175 14210 14297 14700 14790 14994 15138 15225 15300 15435 15660 15876 16065 16443 16660 16820 17052 17150 17255 17493 17661 17748 17850 18270 18522 18900 19278 19575 19845 19894 20300 20580 20706 20825 21025 21315 21420 21924 22050 22185 22491 22707 22950 23324 23490 23548 24157 24389 24650 24990 25230 25578 25725 26100 26460 26622 26775 27405 27540 27783 28350 28420 28594 29155 29435 29580 29841 29988 30276 30450 30870 31059 32130 32886 33075 34300 34425 34510 34986 35322 35525 35700 36540 36975 37044 37485 37845 38367 38556 39150 39690 39788 39933 41209 41412 41650 42050 42630 42891 44100 44370 44982 45414 45675 45900 46305 46980 48195 48314 48778 49300 49735 49980 50460 51156 51450 51765 52479 52983 53244 53550 54810 55566 56700 57188 58310 58725 58870 59682 60900 61740 62118 62475 63075 63945 64260 65772 66150 66555 67473 68121 68850 69020 69972 70644 71050 71485 72471 73167 73950 74970 75690 76734 77175 78300 79380 79866 80325 82215 82418 83300 84100 85260 85782 86275 87465 88305 88740 89523 89964 90828 91350 92610 93177 96390 96628 97556 99225 99470 100079 102900 103530 104958 105966 106575 107100 109620 110925 111132 112455 113535 115101 116620 117450 117740 119364 120785 121945 123627 124236 124950 126150 127890 128673 132300 133110 134946 136242 137025 137700 138915 142100 142970 144942 145775 146334 147175 147900 149205 149940 151380 153468 154350 155295 157437 158949 159732 160650 164430 164836 169099 170723 171564 172550 174930 176610 179046 182700 185220 186354 187425 189225 191835 192780 198450 198940 199665 200158 206045 207060 209916 211932 213150 214455 217413 219501 221850 224910 227070 230202 231525 234900 240975 241570 243890 247254 248675 249900 252300 255780 257346 258825 262395 264915 266220 268569 269892 272484 274050 277830 279531 285940 288463 289884 291550 292668 294350 298410 300237 308700 310590 314874 317898 319725 321300 328860 332775 337365 338198 340605 341446 345100 349860 353220 357425 358092 362355 365835 370881 372708 374850 378450 383670 386019 396900 399330 400316 411075 412090 414613 426300 428910 434826 437325 439002 441525 443700 447615 449820 454140 460404 463050 465885 472311 476847 481950 483140 487780 494508 497350 500395 507297 512169 514692 517650 524790 529830 537138 548100 555660 559062 562275 567675 575505 576926 583100 588700 596820 600474 603925 609725 618135 621180 629748 635796 639450 643365 652239 658503 665550 674730 676396 681210 682892 694575 700553 707281 714850 724710 731670 741762 746025 749700 756900 767340 772038 776475 787185 794745 798660 805707 822150 824180 829226 845495 853615 857820 865389 869652 874650 878004 883050 895230 900711 926100 931770 944622 953694 959175 963900 994700 998325 1000790 1014594 1024338 1030225 1035300 1049580 1059660 1072275 1074276 1087065 1097505 1112643 1118124 1124550 1135350 1151010 1153852 1158057 1195061 1200948 1207850 1219450 1236270 1243839 1278900 1286730 1304478 1311975 1317006 1324575 1331100 1342845 1349460 1362420 1389150 1397655 1401106 1414562 1429700 1442315 1449420 1463340 1483524 1492050 1501185 1521891 1536507 1544076 1552950 1574370 1589490 1611414 1644300 1658452 1686825 1690990 1703025 1707230 1730778 1749300 1766100 1790460 1801422 1811775 1829175 1854405 1863540 1889244 1907388 1918350 1930095 1956717 1975509 1996650 2001580 2029188 2048676 2060450 2073065 2101659 2121843 2144550 2174130 2195010 2225286 2238075 2249100 2270700 2302020 2316114 2329425 2361555 2384235 2390122 2415700 2438900 2472540 2487678 2501975 2536485 2560845 2573460 2596167 2608956 2623950 2634012 2649150 2685690 2702133 2778300 2795310 2802212 2829124 2877525 2884630 2902291 2984100 3002370 3043782 3073014 3090675 3105900 3148740 3178980 3216825 3222828 3261195 3292515 3337929 3373650 3381980 3406050 3414460 3461556 3502765 3536405 3585183 3602844 3623550 3658350 3708810 3731517 3836700 3860190 3913434 3935925 3951018 3973725 3993300 4028535 4120900 4146130 4203318 4227475 4243686 4268075 4289100 4326945 4348260 4390020 4450572 4476150 4503555 4565673 4609521 4632228 4658850 4723110 4768470 4780244 4903871 4950967 4975356 5003950 5072970 5121690 5192334 5247900 5298300 5371380 5404266 5435325 5487525 5563215 5590620 5755050 5769260 5790285 5804582 5975305 6004740 6087564 6146028 6181350 6219195 6304977 6365529 6433650 6522390 6585030 6675858 6714225 6747300 6812100 6988275 7005530 7072810 7170366 7211575 7247100 7316700 7417620 7463034 7505925 7609455 7682535 7720380 7788501 7826868 7871850 7902036 7947450 8057070 8106399 8292260 8365427 8406636 8454950 8487372 8536150 8653890 8706873 8952300 9007110 9131346 9219042 9272025 9317700 9446220 9536940 9650475 9783585 9807742 9877545 9901934 10007900 10145940 10243380 10365325 10384668 10508295 10609215 10755549 10808532 10870650 10975050 11126430 11194551 11510100 11580570 11609164 11807775 11921175 11950610 12023777 12362700 12438390 12609954 12682425 12731058 12804225 12867300 12980835 13044780 13170060 13351716 13428450 13510665 13697019 13828563 13976550 14011060 14145620 14340732 14423150 14511455 14711613 14852901 14926068 15011850 15218910 15365070 15577002 15743700 15894900 16114140 16212798 16305975 16462575 16689645 16730854 16909900 17072300 17307780 17413746 17513825 17682025 17925915 18014220 18262692 18438084 18544050 18657585 18914931 19096587 19300950 19567170 19615484 19755090 19803868 20142675 20316037 20511149 20730650 21016590 21218430 21511098 21634725 21741300 21950100 22252860 22389102 22517775 22828365 23047605 23161140 23365503 23615550 23842350 23901220 24047554 24519355 24754835 24876780 25096281 25219908 25364850 25462116 25608450 25961670 26120619 26856900 27021330 27394038 27657126 27816075 27953100 28846300 28951425 29022910 29423226 29705802 29876525 30023700 30437820 30730140 31095975 31154004 31524885 31827645 32266647 32425596 32611950 32925150 33379290 33461708 33583653 34656769 34827492 35027650 35364050 35851830 36071331 37088100 37315170 37829862 38047275 38193174 38412675 38601900 38942505 39134340 39510180 40285350 40531995 40632074 41022298 41461300 41827135 42033180 42436860 43022196 43269450 43534365 44134839 44558703 44778204 45035550 45656730 46095210 46731006 47231100 47684700 48095108 48917925 49038710 49387725 49509670 50192562 50729700 51216900 51923340 52241238 52541475 53046075 53777745 54042660 54788076 55314252 55632150 55972755 56744793 57289761 57902850 58045820 58846452 59411604 59753050 60118885 60948111 61533447 62191950 63049770 63655290 64533294 64904175 65223900 65850300 66758580 67167306 67553325 68485095 69142815 69313538 70055300 70728100 71703660 72142662 72557275 73558065 74264505 74630340 75288843 75659724 76094550 76386348 76825350 77885010 78361857 80570700 81063990 81264148 82044596 83448225 83654270 84166439 86538900 87068730 88269678 89117406 89629575 90071100 91313460 92190420 93287925 93462012 94574655 95482935 96799941 97835850 98077420 98775450 99019340 100385124 101580185 102555745 103970307 104482476 105082950 106092150 107555490 108213993 111264300 111945510 113489586 114141825 114579522 115238025 115805700 116827515 119506100 120237770 121896222 122596775 123066894 123774175 124383900 125481405 126099540 127310580 129066588 129808350 130603095 132404517 133676109 134334612 135106650 136970190 138285630 138627076 142212259 143578043 144285324 145114550 147116130 148529010 150577686 152189100 153650700 155770020 156723714 157624425 159138225 161333235 162127980 166896450 167308540 167918265 168332878 173283845 174137460 176539356 178234812 179259150 180356655 182844333 184600341 186575850 189149310 190965870 193599882 194712525 195671700 197550900 202659975 203160370 205111490 207940614 209135675 210165900 212184300 215110980 216427986 217671825 220674195 222793515 223891020 225866529 226979172 228283650 229159044 230476050 233655030 235085571 240475540 242597383 243792444 245193550 246133788 247548350 250962810 252499317 259616700 261206190 264809034 267352218 268888725 270213300 273940380 276571260 279863775 283723965 284424518 286448805 287156086 290229100 294232260 297058020 300594425 301155372 304740555 307667235 311910921 313447428 315248850 318276450 322666470 324641979 333792900 335836530 336665756 342425475 345714075 346567690 348689533 358518300 360713310 365688666 367790325 369200682 371322525 373151700 376444215 378298620 381931740 387199764 389425050 391809285 397213551 401028327 405319950 406320740 410222980 415881228 418271350 420832195 426636777 430734129 432855972 435343650 441348390 445587030 451733058 456567300 460952100 467310060 470171142 472873275 477414675 483999705 485194766 490387100 495096700 501925620 504998634 507900925 512778725 519851535 522412380 529618068 534704436 537777450 541069965 548532999 553801023 559727550 567447930 568849036 572897610 574312172 584137575 589165073 601188850 609481110 615334470 623821842 627407025 630497700 636552900 645332940 649283958 653015475 662022585 668380545 671673060 677599587 684850950 691428150 693135380 697379066 711061295 717890215 721426620 727792149 731377332 735580650 738401364 742645050 752888430 757497951 778850100 783618570 794427102 802056654 806666175 810639900 836542700 839591325 841664390 853273554 861468258 866419225 870687300 882696780 891174060 901783275 903466116 914221665 923001705 935732763 940342284 945746550 954829350 967999410 970389532 973925937 1005046301 1009997268 1015801850 1025557450 1039703070 1046068599 1075554900 1082139930 1097065998 1103370975 1107602046 1113967575 1119455100 1129332645 1134895860 1145795220 1168275150 1175427855 1178330146 1202377700 1212986915 1218962220 1230668940 1247643684 1254814050 1262496585 1279910331 1292202387 1298567916 1306030950 1324045170 1336761090 1355199174 1369701900 1382856300 1394758132 1418619825 1422122590 1432244025 1435780430 1455584298 1471161300 1485290100 1505776860 1514995902 1523702775 1538336175 1559554605 1567237140 1588854204 1604113308 1613332350 1623209895 1645598997 1661403069 1679182650 1683328780 1706547108 1722936516 1732838450 1743447665 1767495219 1803566550 1828443330 1846003410 1871465526 1882221075 1891493100 1909658700 1935998820 1947851874 1959046425 1986067755 2005141635 2010092602 2031603700 2051114900 2079406140 2092137198 2104160975 2133183885 2153670645 2164279860 2183376447 2194131996 2206741950 2215204092 2227935150 2258665290 2272493853 2336550300 2350855710 2356660292 2419998525 2425973830 2440826731 2509628100 2524993170 2559820662 2584404774 2599257675 2612061900 2648090340 2673522180 2705349825 2710398348 2742664995 2769005115 2807198289 2837239650 2844245180 2864488050 2871560860 2911168596 2945825365 3015138903 3029991804 3047405550 3076672350 3119109210 3138205797 3226664700 3246419790 3291197994 3310112925 3322806138 3341902725 3358365300 3387997935 3465676900 3486895330 3534990438 3555306475 3589451075 3607133100 3638960745 3656886660 3692006820 3742931052 3764442150 3787489755 3839730993 3876607161 3895703748 3918092850 3972135510 4010283270 4020185204 4124155511 4184274396 4208321950 4266367770 4307341290 4366752894 4413483900 4455870300 4517330580 4544987706 4571108325 4615008525 4678663815 4701711420 4839997050 4851947660 4869629685 4881653462 5025231505 5049986340 5119641324 5168809548 5198515350 5230342995 5302485657 5410699650 5485329990 5538010230 5614396578 5646663225 5674479300 5728976100 5877139275 5891650730 6030277806 6064934575 6094811100 6153344700 6238218420 6276411594 6312482925 6399551655 6461011935 6492839580 6550129341 6582395988 6620225850 6645612276 6683805450 6775995870 6817481559 6973790660 7035324107 7069980876 7110612950 7178902150 7277921490 7322480193 7528884300 7574979510 7679461986 7753214322 7797773025 7836185700 7944271020 8020566540 8116049475 8227994985 8248311022 8307015345 8416643900 8532735540 8614682580 8717238325 8733505788 8837476095 9045416709 9089975412 9142216650 9230017050 9357327630 9414617391 9679994100 9739259370 9763306924 9930338775 10025708175 10050463010 10397030700 10460685990 10604971314 10665919425 10768353225 10821399300 10916882235 10970659980 11076020460 11228793156 11293326450 11362469265 11519192979 11629821483 11754278550 11783301460 12060555612 12129869150 12204133655 12372466533 12552823188 12624965850 12799103310 12922023870 13100258682 13240451700 13367610900 13551991740 13634963118 13713324975 13845025575 14035991445 14070648214 14221225900 14357804300 14555842980 14644960386 14729126825 15075694515 15149959020 15358923972 15506428644 15595546050 15691028985 15907456971 16232098950 16455989970 16496622044 16614030690 16939989675 17085787117 17434476650 17674952190 18090833418 18194803725 18284433300 18460034100 18714655260 18829234782 18937448775 19198654965 19383035805 19478518740 19650388023 19860677550 20051416350 20100926020 20620777555 20921371980 21105972321 21209942628 21331838850 21536706450 21833764470 21967440579 22586652900 22724938530 23038385958 23259642966 23393319075 23508557100 24259738300 24348148425 24408267310 24744933066 25126157525 25249931700 25598206620 25844047740 26151714975 26200517364 26512428285 27136250127 27269926236 27426649950 27690051150 28071982890 28141296428 28243852173 29289920772 29458253650 30151389030 31191092100 31382057970 31814913942 31997758275 32305059675 32464197900 32750646705 32911979940 33228061380 33879979350 34087407795 34171574234 34868953300 35176620535 35349904380 36181666836 36389607450 36612400965 37117399599 37658469564 37874897550 38397309930 38766071610 39300776046 39721355100 40102832700 41139974925 41241555110 41535076725 42211944642 42663677700 43073412900 43667528940 43934881158 44187380475 45227083545 45449877060 46076771916 46519285932 46786638150 47073086955 47722370913 48696296850 48816534620 49489866132 50252315050 51257361351 52303429950 53024856570 54272500254 54584411175 54853299900 55380102300 56143965780 56487704346 56812346325 57595964895 58149107415 58916507300 60302778060 61020668275 61862332665 62764115940 63317916963 63629827884 63995516550 64610119350 65501293410 65902321737 67759958700 68174815590 68343148468 70179957225 70353241070 72779214900 73224801930 74234799198 75378472575 75749795100 76794619860 77532143220 78455144925 78601552092 79537284855 81408750381 82279949850 82483110220 83070153450 84423889284 85428935585 87869762316 88374760950 90454167090 93573276300 94146173910 95444741826 95993274825 96915179025 97392593700 98251940115 100504630100 102514722702 103103887775 104606859900 105529861605 106049713140 108545000508 109168822350 109837202895 111352198797 112975408692 113624692650 115191929790 116298214830 119600509819 122041336550 123724665330 126635833926 127991033100 129220238700 131002586820 131804643474 132562141425 135681250635 136349631180 140359914450 140706482140 141219260865 146449603860 148469598396 150756945150 153772084053 156910289850 159074569710 162817500762 163753233525 164559899700 166140306900 170437038975 170857871170 175883102675 176749521900 180908334180 183062004825 185586997995 188292347820 189953750889 190889483652 191986549650 193830358050 196503880230 197706965211 205029445404 206207775550 211059723210 218337644700 219674405790 222704397594 226135417725 227249385300 230383859580 232596429660 235365434775 238611854565 239201019638 244082673100 247449330660 253271667852 256286806755 263609286948 265124282850 271362501270 280719828900 282438521730 287979824475 290745537075 301513890300 307544168106 309311663325 313820579700 316589584815 318149139420 325635001524 327506467050 329511608685 334056596391 340874077950 341715742340 351766205350 358801529457 366124009650 371173995990 379907501778 383973099300 387660716100 393007760460 395413930422 397686424275 407043751905 412415551100 422119446420 427144677925 439348811580 445408795188 452270835450 461316252159 470730869550 477223709130 478402039276 491259700575 512573613510 527649308025 530248565700 542725002540 549186014475 556760993985 564877043460 569861252667 575959648950 581491074150 598002549095 615088336212 618623326650 633179169630 655012934100 659023217370 668113192782 678406253175 681748155900 703532410700 706096304325 717603058914 732248019300 742347991980 759815003556 768860420265 790827860844 795372848550 814087503810 854289355850 904541670900 922632504318 927934989975 941461739100 949768754445 954447418260 982519401150 988534826055 1025147227020 1055298616050 1076404588371 1098372028950 1113521987970 1139722505334 1151919297900 1162982148300 1193059272825 1196005098190 1237246653300 1266358339260 1281434033775 1318046434740 1336226385564 1356812506350 1383948756477 1412192608650 1435206117828 1537720840530 1582947924075 1590745697100 1628175007620 1647558043425 1670282981955 1708578711700 1794007647285 1845265008636 1855869979950 1899537508890 1965038802300 1977069652110 2035218759525 2110597232100 2152809176742 2196744057900 2227043975940 2279445010668 2306581260795 2386118545650 2392010196380 2562868067550 2713625012700 2767897512954 2783804969925 2824385217300 2849306263335 2990012745475 3075441681060 3165895848150 3229213765113 3295116086850 3340565963910 3588015294570 3711739959900 3799075017780 3844302101325 3954139304220 4070437519050 4305618353484 4613162521590 4748843772225 4772237091300 4942674130275 5125736135100 5382022941855 5535795025908 5567609939850 5698612526670 5980025490950 6331791696300 6458427530226 6590232173700 6681131927820 6919743782385 7176030589140 7688604202650 8140875038100 8351414909775 8970038236425 9226325043180 9497687544450 9687641295339 9885348260550 10764045883710 11135219879700 11397225053340 11532906303975 11960050981900 12916855060452 13839487564770 14246531316675 15377208405300 16146068825565 16702829819550 17940076472850 18995375088900 19375282590678 19770696521100 21528091767420 23065812607950 26910114709275 27678975129540 28493062633350 32292137651130 33405659639100 34598718911925 35880152945700 38750565181356 46131625215900 48438206476695 53820229418550 56986125266700 64584275302260 69197437823850 80730344127825 96876412953390 107640458837100 138394875647700 161460688255650 193752825906780 242191032383475 322921376511300 484382064766950 968764129533900
- Sum of all divisors σ(n): 4016128091976000
- Sum of proper divisors (its aliquot sum) s(n): 3047363962442100
- 968764129533900 is an abundant number, because the sum of its proper divisors (3047363962442100) is greater than itself. Its abundance is 2078599832908200
Bases of 968764129533900
- Binary: 110111000100010101111110011100111111011111110011002
- Hexadecimal: 0x37115F9CFDFCC
- Base-36: 9JEC3HZ4R0
Squares and roots of 968764129533900
- 968764129533900 squared (9687641295339002) is 938503938671574978231249210000
- 968764129533900 cubed (9687641295339003) is 909188951211305003701143982385252043219000000
-
The
square root of 968764129533900 is 31124975.9764389215 -
The
cube root of 968764129533900 is 98947.7712991437
Scales and comparisons
How big is 968764129533900?- 968,764,129,533,900 seconds is equal to 30,803,702 years, 38 weeks, 1 day, 12 hours, 45 minutes.
-
To count from 1 to 968,764,129,533,900 would take you about seventy-seven million, nine thousand, two hundred fifty-six 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 968764129533900 cubic inches would be around 8245.6 feet tall.
Recreational maths with 968764129533900
- 968764129533900 backwards is 009335921467869
- The number of decimal digits it has is: 15
- The sum of 968764129533900's digits is 72
- 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 968764129533900 - Facts about the integer". Numbermatics.com. 2024. Web. 11 May 2024.
APA style:
Numbermatics. (2024). Number 968764129533900 - Facts about the integer. Retrieved 11 May 2024, from https://numbermatics.com/n/968764129533900/
Chicago style:
Numbermatics. 2024. "Number 968764129533900 - Facts about the integer". https://numbermatics.com/n/968764129533900/
The information we have on file for 968764129533900 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 968764129533900, math, Factors of 968764129533900, curriculum, school, college, exams, university, Prime factorization of 968764129533900, STEM, science, technology, engineering, physics, economics, calculator, nine hundred sixty-eight trillion, seven hundred sixty-four billion, one hundred twenty-nine million, five hundred thirty-three thousand, nine hundred.