32231492298561600
32,231,492,298,561,600 is an even composite number composed of seven prime numbers multiplied together.
What does the number 32231492298561600 look like?
This visualization shows the relationship between its 7 prime factors (large circles) and 2016 divisors.
32231492298561600 is an even composite number. It is composed of seven distinct prime numbers multiplied together. It has a total of two thousand and sixteen divisors.
Prime factorization of 32231492298561600:
26 × 33 × 52 × 112 × 421 × 1553 × 9431
(2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5 × 11 × 11 × 421 × 1553 × 9431)See below for interesting mathematical facts about the number 32231492298561600 from the Numbermatics database.
Names of 32231492298561600
- Cardinal: 32231492298561600 can be written as Thirty-two quadrillion, two hundred thirty-one trillion, four hundred ninety-two billion, two hundred ninety-eight million, five hundred sixty-one thousand, six hundred.
Scientific notation
- Scientific notation: 3.22314922985616 × 1016
Factors of 32231492298561600
Divisors of 32231492298561600
- Number of divisors d(n): 2016
-
Complete list of divisors:
1 2 3 4 5 6 8 9 10 11 12 15 16 18 20 22 24 25 27 30 32 33 36 40 44 45 48 50 54 55 60 64 66 72 75 80 88 90 96 99 100 108 110 120 121 132 135 144 150 160 165 176 180 192 198 200 216 220 225 240 242 264 270 275 288 297 300 320 330 352 360 363 396 400 421 432 440 450 480 484 495 528 540 550 576 594 600 605 660 675 704 720 726 792 800 825 842 864 880 900 960 968 990 1056 1080 1089 1100 1188 1200 1210 1263 1320 1350 1440 1452 1485 1553 1584 1600 1650 1684 1728 1760 1800 1815 1936 1980 2105 2112 2160 2178 2200 2376 2400 2420 2475 2526 2640 2700 2880 2904 2970 3025 3106 3168 3267 3300 3368 3520 3600 3630 3789 3872 3960 4210 4320 4356 4400 4631 4659 4752 4800 4840 4950 5052 5280 5400 5445 5808 5940 6050 6212 6315 6336 6534 6600 6736 7200 7260 7425 7578 7744 7765 7920 8420 8640 8712 8800 9075 9262 9318 9431 9504 9680 9900 10104 10525 10560 10800 10890 11367 11616 11880 12100 12424 12630 13068 13200 13472 13893 13977 14400 14520 14850 15156 15530 15840 16335 16840 17083 17424 17600 18150 18524 18636 18862 18945 19008 19360 19800 20208 21050 21600 21780 22734 23155 23232 23295 23760 24200 24848 25260 26136 26400 26944 27225 27786 27954 28293 29040 29700 30312 31060 31575 31680 32670 33680 34166 34848 36300 37048 37272 37724 37890 38720 38825 39600 40416 41679 41931 42100 43200 43560 45468 46310 46590 47155 47520 48400 49696 50520 50941 51249 52272 52800 54450 55572 55908 56586 56835 58080 59400 60624 62120 63150 65340 67360 68332 69465 69696 69885 72600 74096 74544 75448 75780 77650 79200 80832 81675 83358 83862 84200 84879 85415 87120 90936 92620 93180 94310 94725 95040 96800 99392 101040 101882 102498 103741 104544 108900 111144 111816 113172 113670 115775 116160 116475 118800 121248 124240 125037 126300 130680 134720 136664 138930 139770 141465 145200 148192 149088 150896 151560 152823 153747 155300 158400 163350 166716 167724 168400 169758 170830 174240 181872 185240 186360 187913 188620 189450 193600 202080 203764 204996 207482 208395 209088 209655 217800 222288 223632 226344 227340 231550 232950 235775 237600 242496 248480 250074 252600 254637 254705 256245 261360 273328 277860 279540 282930 284175 290400 296384 298176 301792 303120 305646 307494 310600 311223 326700 333432 335448 336800 339516 341660 347325 348480 349425 363744 370480 372720 375826 377240 378900 404160 407528 409992 414964 416790 419310 424395 427075 435600 444576 447264 452688 454680 458469 461241 463100 465900 471550 475200 496960 500148 505200 509274 509410 512490 518705 522720 546656 555720 559080 563739 565860 568350 580800 603584 606240 611292 614988 621200 622446 625185 653400 653813 666864 670896 673600 679032 683320 694650 698850 707325 727488 740960 745440 751652 754480 757800 764115 768735 815056 819984 829928 833580 838620 848790 854150 871200 889152 894528 905376 909360 916938 922482 926200 931800 933669 939565 943100 1000296 1010400 1018548 1018820 1024980 1037410 1041975 1045440 1048275 1093312 1111440 1118160 1127478 1131720 1136700 1141151 1212480 1222584 1229976 1242400 1244892 1250370 1273185 1273525 1281225 1306800 1307626 1333728 1341792 1358064 1366640 1375407 1389300 1397700 1414650 1481920 1490880 1503304 1508960 1515600 1528230 1537470 1556115 1630112 1639968 1659856 1667160 1677240 1691217 1697580 1708300 1742400 1810752 1818720 1833876 1844964 1852400 1863600 1867338 1879130 1886200 1961439 2000592 2020800 2037096 2037640 2049960 2074820 2083950 2096550 2121975 2222880 2236320 2254956 2263440 2273400 2282302 2292345 2306205 2445168 2459952 2484800 2489784 2500740 2546370 2547050 2562450 2593525 2613600 2615252 2667456 2683584 2716128 2733280 2750814 2778600 2795400 2801007 2818695 2829300 3006608 3017920 3031200 3056460 3074940 3112230 3125925 3260224 3269065 3279936 3319712 3334320 3354480 3382434 3395160 3416600 3423453 3637440 3667752 3689928 3704800 3727200 3734676 3758260 3772400 3820575 3843675 3922878 3970451 4001184 4074192 4075280 4099920 4149640 4167900 4193100 4243950 4445760 4472640 4509912 4526880 4546800 4564604 4584690 4612410 4668345 4697825 4890336 4919904 4979568 5001480 5073651 5092740 5094100 5124900 5187050 5227200 5230504 5432256 5466560 5501628 5557200 5590800 5602014 5637390 5658600 5705755 5884317 6013216 6062400 6112920 6149880 6224460 6251850 6365925 6538130 6639424 6668640 6708960 6764868 6790320 6833200 6846906 6877035 7191943 7335504 7379856 7409600 7454400 7469352 7516520 7544800 7641150 7687350 7780575 7845756 7940902 8002368 8148384 8150560 8199840 8299280 8335800 8386200 8456085 8487900 9019824 9053760 9093600 9129208 9169380 9224820 9336690 9395650 9780672 9807195 9839808 9959136 10002960 10147302 10185480 10188200 10249800 10270359 10374100 10461008 11003256 11114400 11181600 11204028 11274780 11317200 11411510 11461725 11531025 11768634 11911353 12026432 12225840 12299760 12448920 12503700 12731850 13076260 13337280 13417920 13529736 13580640 13666400 13693812 13754070 14005035 14093475 14383886 14646343 14671008 14759712 14938704 15033040 15089600 15282300 15374700 15561150 15691512 15881804 16296768 16301120 16345325 16399680 16598560 16671600 16772400 16912170 16975800 17117265 17652951 18039648 18187200 18258416 18338760 18449640 18673380 18791300 19614390 19852255 19918272 20005920 20294604 20370960 20376400 20499600 20540718 20748200 20922016 21575829 22006512 22228800 22363200 22408056 22549560 22634400 22823020 22923450 23062050 23341725 23537268 23822706 24451680 24599520 24897840 25007400 25368255 25463700 26152520 27059472 27161280 27332800 27387624 27508140 28010070 28186950 28528775 28767772 29292686 29342016 29421585 29519424 29877408 30066080 30564600 30749400 30811077 31122300 31383024 31763608 32690650 33197120 33343200 33544800 33824340 33951600 34234530 34385175 35305902 35734059 35959715 36079296 36516832 36677520 36899280 37346760 37582600 39228780 39704510 40011840 40589208 40741920 40752800 40999200 41081436 41496400 41844032 42280425 43151658 43674961 43939029 44013024 44816112 45099120 45268800 45646040 45846900 46124100 46683450 47074536 47645412 48903360 49035975 49199040 49795680 50014800 50736510 50927400 51351795 52305040 54118944 54775248 55016280 56020140 56373900 57057550 57535544 58585372 58843170 59556765 59754816 60132160 61129200 61498800 61622154 62244600 62766048 63527216 64727487 65381300 66686400 67089600 67648680 67903200 68469060 68770350 70025175 70611804 71468118 71919430 73033664 73231715 73355040 73798560 74693520 75165200 78457560 79111373 79409020 81178416 81483840 81505600 81998400 82162872 82992800 84560850 85586325 86303316 87349922 87878058 88026048 88264755 89632224 90198240 91292080 91693800 92248200 93366900 94149072 95290824 98071950 99261275 99591360 100029600 101473020 101854800 102703590 104610080 107202177 107879145 108237888 109550496 110032560 112040280 112747800 114115100 115071088 117170744 117686340 119113530 122258400 122997600 123244308 124489200 125532096 126841275 127054432 129454974 130762600 131024883 131817087 135297360 135806400 136938120 137540700 140050350 141223608 142936236 143838860 146463430 146710080 147107925 147597120 149387040 150330400 154055385 156915120 158222746 158818040 161109773 162356832 164325744 165985600 169121700 171172650 172606632 174699844 175756116 176529510 178670295 179264448 179798575 180396480 182584160 183387600 184496400 186733800 188298144 190581648 194182461 196143900 198522550 200059200 202946040 203709600 205407180 209220160 214404354 215758290 218374805 219100992 219695145 220065120 224080560 225495600 228230200 230142176 234341488 235372680 237334119 238227060 244516800 245995200 246488616 248978400 253682550 254108864 256758975 258909948 261525200 262049766 263634174 270594720 273876240 275081400 280100700 282447216 285872472 287677720 292926860 294215850 297783825 298774080 300660800 308110770 313830240 316445492 317636080 322219546 323637435 324713664 328651488 338243400 342345300 345213264 349399688 351512232 353059020 357340590 359597150 365168320 366158575 366775200 368992800 373467600 376596288 381163296 388364922 392287800 393074649 395451261 395556865 397045100 405892080 407419200 410814360 428808708 431516580 436749610 439390290 440130240 441323775 448161120 450991200 456460400 460284352 468682976 470745360 474668238 476454120 480424571 483329319 492977232 497956800 507365100 513517950 517819896 523050400 524099532 527268348 536010885 539395725 541189440 547752480 550162800 560201400 564894432 571744944 575355440 585853720 588431700 595567650 616221540 627660480 632890984 635272160 644439092 647274870 655124415 657302976 659085435 676486800 684690600 690426528 698799376 703024464 706118040 712002357 714681180 719194300 732317150 733550400 737985600 746935200 762326592 770276925 776729844 784575600 786149298 790902522 791113730 794090200 805548865 811784160 821628720 857617416 863033160 873499220 878780580 882647550 893351475 896322240 901982400 912920800 937365952 941490720 949336476 952908240 960849142 966658638 970912305 985954464 1014730200 1027035900 1035639792 1046100800 1048199064 1054536696 1072021770 1078791450 1091874025 1095504960 1098475725 1100325600 1120402800 1129788864 1143489888 1150710880 1171707440 1176863400 1179223947 1186670595 1191135300 1232443080 1265781968 1270544320 1288878184 1294549740 1310248830 1318170870 1352973600 1369381200 1380853056 1397598752 1406048928 1412236080 1424004714 1429362360 1438388600 1441273713 1449987957 1464634300 1493870400 1540553850 1553459688 1569151200 1572298596 1581805044 1582227460 1588180400 1611097730 1618187175 1623568320 1643257440 1715234832 1726066320 1746998440 1757561160 1765295100 1772207503 1786702950 1825841600 1882981440 1898672952 1905816480 1921698284 1933317276 1941824610 1965373245 1971908928 1977256305 1977784325 2029460400 2054071800 2071279584 2096398128 2109073392 2136007071 2144043540 2157582900 2183748050 2196951450 2200651200 2240805600 2286979776 2301421760 2343414880 2353726800 2358447894 2373341190 2382270600 2402122855 2416646595 2464886160 2531563936 2577756368 2589099480 2620497660 2636341740 2680054425 2705947200 2738762400 2795197504 2812097856 2824472160 2848009428 2858724720 2876777200 2882547426 2899975914 2929268600 3081107700 3106919376 3138302400 3144597192 3163610088 3164454920 3176360800 3222195460 3236374350 3275622075 3286514880 3295427175 3430469664 3452132640 3493996880 3515122320 3530590200 3544415006 3560011785 3573405900 3797345904 3811632960 3843396568 3866634552 3883649220 3930746490 3954512610 3955568650 4027744325 4058920800 4108143600 4142559168 4192796256 4218146784 4272014142 4288087080 4315165800 4323821139 4349963871 4367496100 4393902900 4481611200 4686829760 4707453600 4716895788 4746682380 4764541200 4804245710 4833293190 4854561525 4929772320 5063127872 5155512736 5178198960 5240995320 5272683480 5316622509 5360108850 5477524800 5648944320 5696018856 5717449440 5753554400 5765094852 5799951828 5858537200 5896119735 5933352975 6162215400 6166110403 6213838752 6289194384 6327220176 6328909840 6352721600 6444390920 6472748700 6551244150 6590854350 6860939328 6904265280 6987993760 7030244640 7061180400 7088830012 7120023570 7146811800 7206368565 7249939785 7594691808 7686793136 7733269104 7767298440 7861492980 7909025220 7911137300 8055488650 8117841600 8216287200 8385592512 8436293568 8544028284 8576174160 8630331600 8647642278 8699927742 8734992200 8787805800 8861037515 9414907200 9433791576 9493364760 9529082400 9608491420 9666586380 9709123050 9826866225 9859544640 9886281525 10311025472 10356397920 10481990640 10545366960 10633245018 10680035355 10720217700 11392037712 11434898880 11507108800 11530189704 11599903656 11717074400 11792239470 11866705950 12010614275 12083232975 12324430800 12332220806 12427677504 12578388768 12654440352 12657819680 12888781840 12945497400 12971463417 13102488300 13181708700 13975987520 14060489280 14122360800 14177660024 14240047140 14293623600 14412737130 14499879570 15189383616 15373586272 15466538208 15534596880 15722985960 15818050440 15822274600 15949867527 16110977300 16432574400 17088056568 17152348320 17260663200 17295284556 17399855484 17469984400 17575611600 17722075030 17800058925 18498331209 18867583152 18986729520 19058164800 19216982840 19333172760 19418246100 19653732450 19772563050 20712795840 20963981280 21090733920 21266490036 21360070710 21440435400 21619105695 21749819355 22784075424 23060379408 23199807312 23434148800 23584478940 23733411900 24021228550 24166465950 24648861600 24664441612 25156777536 25308880704 25315639360 25777563680 25890994800 25942926834 26204976600 26363417400 26583112545 28244721600 28355320048 28480094280 28587247200 28825474260 28999759140 29480598675 30747172544 30830552015 30933076416 31069193760 31445971920 31636100880 31644549200 31899735054 32221954600 34176113136 34304696640 34521326400 34590569112 34799710968 34939968800 35151223200 35444150060 35600117850 36031842825 36249698925 36996662418 37735166304 37973459040 38433965680 38666345520 38836492200 39307464900 39545126100 41927962560 42181467840 42532980072 42720141420 42880870800 43238211390 43499638710 44305187575 45568150848 46120758816 46399614624 47168957880 47466823800 47849602581 48042457100 48332931900 49297723200 49328883224 51555127360 51781989600 51885853668 52409953200 52726834800 53166225090 53400176775 55494993627 56710640096 56960188560 57174494400 57650948520 57999518280 58961197350 61661104030 62138387520 62891943840 63272201760 63289098400 63799470108 64443909200 64857317085 67827214433 68352226272 69181138224 69599421936 69879937600 70302446400 70888300120 71200235700 72063685650 72499397850 73993324836 75470332608 75946918080 76867931360 77332691040 77672984400 78614929800 79090252200 79749337635 85065960144 85440282840 85761741600 86476422780 86999277420 88610375150 92241517632 92491656045 92799229248 94337915760 94933647600 95699205162 96084914200 96665863800 98657766448 103563979200 103771707336 104819906400 105453669600 106332450180 106800353550 108095528475 108749096775 110989987254 113421280192 113920377120 115301897040 115999036560 117922394700 123322208060 125783887680 126544403520 126578196800 127598940216 128887818400 129714634170 132915562725 135654428866 136704452544 138362276448 139198843872 141776600240 142400471400 144127371300 144998795700 147986649672 153735862720 154152760075 154665382080 155345968800 157229859600 158180504400 159498675270 166484980881 170131920288 170880565680 171523483200 172952845560 173998554840 177220750300 184983312090 188675831520 189867295200 191398410324 192169828400 193331727600 197315532896 203481643299 207543414672 209639812800 210907339200 212664900360 213600707100 216191056950 217498193550 221979974508 227840754240 230603794080 231998073120 235844789400 239248012905 246644416120 255197880432 257775636800 259429268340 265831125450 271308857732 276724552896 277474968135 278397687744 283553200480 284800942800 288254742600 289997591400 295973299344 308305520150 310691937600 314459719200 316361008800 318997350540 324286585425 332969961762 339136072165 340263840576 341761131360 345905691120 347997109680 354441500600 369966624180 377351663040 379734590400 382796820648 384339656800 386663455200 394631065792 398746688175 406963286598 415086829344 425329800720 427201414200 432382113900 434996387100 443959949016 461207588160 462458280225 463996146240 471689578800 478496025810 493288832240 510395760864 518858536680 531662250900 542617715464 554949936270 567106400960 569601885600 576509485200 579995182800 591946598688 610444929897 616611040300 628919438400 632722017600 637994701080 648573170850 665939923524 678272144330 683522262720 691811382240 695994219360 708883001200 739933248360 746099358763 765593641296 768679313600 773326910400 797493376350 813926573196 830173658688 832424904405 850659601440 854402828400 864764227800 869992774200 887919898032 924916560450 943379157600 956992051620 986577664480 1017408216495 1020791521728 1037717073360 1063324501800 1085235430928 1109899872540 1139203771200 1153018970400 1159990365600 1183893197376 1196240064525 1220889859794 1233222080600 1275989402160 1297146341700 1331879847048 1356544288660 1383622764480 1387374840675 1391988438720 1417766002400 1479866496720 1492198717526 1531187282592 1594986752700 1627853146392 1664849808810 1695680360825 1701319202880 1708805656800 1729528455600 1739985548400 1775839796064 1831334789691 1849833120900 1886758315200 1913984103240 1973155328960 2034816432990 2075434146720 2126649003600 2170470861856 2219799745080 2238298076289 2306037940800 2319980731200 2392480129050 2441779719588 2466444161200 2551978804320 2594292683400 2663759694096 2713088577320 2774749681350 2835532004800 2959732993440 2984397435052 3052224649485 3062374565184 3189973505400 3255706292784 3329699617620 3391360721650 3417611313600 3459056911200 3479971096800 3551679592128 3662669579382 3699666241800 3730496793815 3827968206480 4069632865980 4150868293440 4162124522025 4253298007200 4340941723712 4439599490160 4476596152578 4784960258100 4883559439176 4932888322400 5087041082475 5103957608640 5188585366800 5327519388192 5426177154640 5549499362700 5919465986880 5968794870104 6104449298970 6379947010800 6511412585568 6659399235240 6714894228867 6782721443300 6918113822400 6959942193600 7325339158764 7399332483600 7460993587630 7655936412960 8139265731960 8324249044050 8506596014400 8879198980320 8953192305156 9156673948455 9569920516200 9767118878352 9865776644800 10174082164950 10377170733600 10655038776384 10852354309280 11098998725400 11191490381445 11937589740208 12208898597940 12759894021600 13022825171136 13318798470480 13429788457734 13565442886600 14650678317528 14798664967200 14921987175260 15261123247425 15311872825920 16278531463920 16648498088100 17758397960640 17906384610312 18313347896910 18652483969075 19139841032400 19534237756704 20144682686601 20348164329900 20754341467200 21704708618560 22197997450800 22382980762890 23875179480416 24417797195880 25519788043200 26637596940960 26859576915468 27130885773200 29301356635056 29597329934400 29843974350520 30522246494850 32557062927840 33296996176200 33574471144335 35812769220624 36626695793820 37304967938150 38279682064800 39068475513408 40289365373202 40696328659800 44395994901600 44765961525780 45783369742275 47750358960832 48835594391760 53275193881920 53719153830936 54261771546400 55957451907225 58602713270112 59687948701040 61044492989700 65114125855680 66593992352400 67148942288670 71625538441248 73253391587640 74609935876300 76559364129600 80578730746404 81392657319600 88791989803200 89531923051560 91566739484550 97671188783520 100723413433005 107438307661872 108523543092800 111914903814450 117205426540224 119375897402080 122088985979400 133187984704800 134297884577340 143251076882496 146506783175280 149219871752600 161157461492808 162785314639200 167872355721675 179063846103120 183133478969100 195342377567040 201446826866010 214876615323744 223829807628900 238751794804160 244177971958800 266375969409600 268595769154680 293013566350560 298439743505200 322314922985616 325570629278400 335744711443350 358127692206240 366266957938200 402893653732020 429753230647488 447659615257800 488355943917600 503617067165025 537191538309360 586027132701120 596879487010400 644629845971232 671489422886700 716255384412480 732533915876400 805787307464040 895319230515600 976711887835200 1007234134330050 1074383076618720 1193758974020800 1289259691942464 1342978845773400 1465067831752800 1611574614928080 1790638461031200 2014468268660100 2148766153237440 2685957691546800 2930135663505600 3223149229856160 3581276922062400 4028936537320200 5371915383093600 6446298459712320 8057873074640400 10743830766187200 16115746149280800 32231492298561600
- Sum of all divisors σ(n): 129552054490333440
- Sum of proper divisors (its aliquot sum) s(n): 97320562191771840
- 32231492298561600 is an abundant number, because the sum of its proper divisors (97320562191771840) is greater than itself. Its abundance is 65089069893210240
Bases of 32231492298561600
- Binary: 11100101000001001011111000110010000100101011000010000002
- Hexadecimal: 0x72825F19095840
- Base-36: 8TD3Z5E3DC0
Squares and roots of 32231492298561600
- 32231492298561600 squared (322314922985616002) is 1038869095792235732953428994560000
- 32231492298561600 cubed (322314922985616003) is 33484301260241099119085751018477169622224896000000
-
The
square root of 32231492298561600 is 179531312.8636940593 -
The
cube root of 32231492298561600 is 318243.9365407547
Scales and comparisons
How big is 32231492298561600?- 32,231,492,298,561,600 seconds is equal to 1,024,861,756 years, 28 weeks, 1 day, 12 hours.
-
To count from 1 to 32,231,492,298,561,600 would take you about three billion, seventy-four million, five hundred eighty-five thousand, two hundred sixty-nine 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 32231492298561600 cubic inches would be around 26520.3 feet tall.
Recreational maths with 32231492298561600
- 32231492298561600 backwards is 00616589229413223
- The number of decimal digits it has is: 17
- The sum of 32231492298561600's digits is 63
- More coming soon!
Link to this page
HTML: To link to this page, just copy and paste the link below into your blog, web page or email.
BBCODE: To link to this page in a forum post or comment box, just copy and paste the link code below:
Cite this page
MLA style:
"Number 32231492298561600 - Facts about the integer". Numbermatics.com. 2024. Web. 23 May 2024.
APA style:
Numbermatics. (2024). Number 32231492298561600 - Facts about the integer. Retrieved 23 May 2024, from https://numbermatics.com/n/32231492298561600/
Chicago style:
Numbermatics. 2024. "Number 32231492298561600 - Facts about the integer". https://numbermatics.com/n/32231492298561600/
The information we have on file for 32231492298561600 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 32231492298561600, math, Factors of 32231492298561600, curriculum, school, college, exams, university, Prime factorization of 32231492298561600, STEM, science, technology, engineering, physics, economics, calculator, thirty-two quadrillion, two hundred thirty-one trillion, four hundred ninety-two billion, two hundred ninety-eight million, five hundred sixty-one thousand, six hundred.