What are the numbers divisible by 90?

90, 180, 270, 360, 450, 540, 630, 720, 810, 900, 990, 1080, 1170, 1260, 1350, 1440, 1530, 1620, 1710, 1800, 1890, 1980, 2070, 2160, 2250, 2340, 2430, 2520, 2610, 2700, 2790, 2880, 2970, 3060, 3150, 3240, 3330, 3420, 3510, 3600, 3690, 3780, 3870, 3960, 4050, 4140, 4230, 4320, 4410, 4500, 4590, 4680, 4770, 4860, 4950, 5040, 5130, 5220, 5310, 5400, 5490, 5580, 5670, 5760, 5850, 5940, 6030, 6120, 6210, 6300, 6390, 6480, 6570, 6660, 6750, 6840, 6930, 7020, 7110, 7200, 7290, 7380, 7470, 7560, 7650, 7740, 7830, 7920, 8010, 8100, 8190, 8280, 8370, 8460, 8550, 8640, 8730, 8820, 8910, 9000, 9090, 9180, 9270, 9360, 9450, 9540, 9630, 9720, 9810, 9900, 9990, 10080, 10170, 10260, 10350, 10440, 10530, 10620, 10710, 10800, 10890, 10980, 11070, 11160, 11250, 11340, 11430, 11520, 11610, 11700, 11790, 11880, 11970, 12060, 12150, 12240, 12330, 12420, 12510, 12600, 12690, 12780, 12870, 12960, 13050, 13140, 13230, 13320, 13410, 13500, 13590, 13680, 13770, 13860, 13950, 14040, 14130, 14220, 14310, 14400, 14490, 14580, 14670, 14760, 14850, 14940, 15030, 15120, 15210, 15300, 15390, 15480, 15570, 15660, 15750, 15840, 15930, 16020, 16110, 16200, 16290, 16380, 16470, 16560, 16650, 16740, 16830, 16920, 17010, 17100, 17190, 17280, 17370, 17460, 17550, 17640, 17730, 17820, 17910, 18000, 18090, 18180, 18270, 18360, 18450, 18540, 18630, 18720, 18810, 18900, 18990, 19080, 19170, 19260, 19350, 19440, 19530, 19620, 19710, 19800, 19890, 19980, 20070, 20160, 20250, 20340, 20430, 20520, 20610, 20700, 20790, 20880, 20970, 21060, 21150, 21240, 21330, 21420, 21510, 21600, 21690, 21780, 21870, 21960, 22050, 22140, 22230, 22320, 22410, 22500, 22590, 22680, 22770, 22860, 22950, 23040, 23130, 23220, 23310, 23400, 23490, 23580, 23670, 23760, 23850, 23940, 24030, 24120, 24210, 24300, 24390, 24480, 24570, 24660, 24750, 24840, 24930, 25020, 25110, 25200, 25290, 25380, 25470, 25560, 25650, 25740, 25830, 25920, 26010, 26100, 26190, 26280, 26370, 26460, 26550, 26640, 26730, 26820, 26910, 27000, 27090, 27180, 27270, 27360, 27450, 27540, 27630, 27720, 27810, 27900, 27990, 28080, 28170, 28260, 28350, 28440, 28530, 28620, 28710, 28800, 28890, 28980, 29070, 29160, 29250, 29340, 29430, 29520, 29610, 29700, 29790, 29880, 29970, 30060, 30150, 30240, 30330, 30420, 30510, 30600, 30690, 30780, 30870, 30960, 31050, 31140, 31230, 31320, 31410, 31500, 31590, 31680, 31770, 31860, 31950, 32040, 32130, 32220, 32310, 32400, 32490, 32580, 32670, 32760, 32850, 32940, 33030, 33120, 33210, 33300, 33390, 33480, 33570, 33660, 33750, 33840, 33930, 34020, 34110, 34200, 34290, 34380, 34470, 34560, 34650, 34740, 34830, 34920, 35010, 35100, 35190, 35280, 35370, 35460, 35550, 35640, 35730, 35820, 35910, 36000, 36090, 36180, 36270, 36360, 36450, 36540, 36630, 36720, 36810, 36900, 36990, 37080, 37170, 37260, 37350, 37440, 37530, 37620, 37710, 37800, 37890, 37980, 38070, 38160, 38250, 38340, 38430, 38520, 38610, 38700, 38790, 38880, 38970, 39060, 39150, 39240, 39330, 39420, 39510, 39600, 39690, 39780, 39870, 39960, 40050, 40140, 40230, 40320, 40410, 40500, 40590, 40680, 40770, 40860, 40950, 41040, 41130, 41220, 41310, 41400, 41490, 41580, 41670, 41760, 41850, 41940, 42030, 42120, 42210, 42300, 42390, 42480, 42570, 42660, 42750, 42840, 42930, 43020, 43110, 43200, 43290, 43380, 43470, 43560, 43650, 43740, 43830, 43920, 44010, 44100, 44190, 44280, 44370, 44460, 44550, 44640, 44730, 44820, 44910, 45000, 45090, 45180, 45270, 45360, 45450, 45540, 45630, 45720, 45810, 45900, 45990, 46080, 46170, 46260, 46350, 46440, 46530, 46620, 46710, 46800, 46890, 46980, 47070, 47160, 47250, 47340, 47430, 47520, 47610, 47700, 47790, 47880, 47970, 48060, 48150, 48240, 48330, 48420, 48510, 48600, 48690, 48780, 48870, 48960, 49050, 49140, 49230, 49320, 49410, 49500, 49590, 49680, 49770, 49860, 49950, 50040, 50130, 50220, 50310, 50400, 50490, 50580, 50670, 50760, 50850, 50940, 51030, 51120, 51210, 51300, 51390, 51480, 51570, 51660, 51750, 51840, 51930, 52020, 52110, 52200, 52290, 52380, 52470, 52560, 52650, 52740, 52830, 52920, 53010, 53100, 53190, 53280, 53370, 53460, 53550, 53640, 53730, 53820, 53910, 54000, 54090, 54180, 54270, 54360, 54450, 54540, 54630, 54720, 54810, 54900, 54990, 55080, 55170, 55260, 55350, 55440, 55530, 55620, 55710, 55800, 55890, 55980, 56070, 56160, 56250, 56340, 56430, 56520, 56610, 56700, 56790, 56880, 56970, 57060, 57150, 57240, 57330, 57420, 57510, 57600, 57690, 57780, 57870, 57960, 58050, 58140, 58230, 58320, 58410, 58500, 58590, 58680, 58770, 58860, 58950, 59040, 59130, 59220, 59310, 59400, 59490, 59580, 59670, 59760, 59850, 59940, 60030, 60120, 60210, 60300, 60390, 60480, 60570, 60660, 60750, 60840, 60930, 61020, 61110, 61200, 61290, 61380, 61470, 61560, 61650, 61740, 61830, 61920, 62010, 62100, 62190, 62280, 62370, 62460, 62550, 62640, 62730, 62820, 62910, 63000, 63090, 63180, 63270, 63360, 63450, 63540, 63630, 63720, 63810, 63900, 63990, 64080, 64170, 64260, 64350, 64440, 64530, 64620, 64710, 64800, 64890, 64980, 65070, 65160, 65250, 65340, 65430, 65520, 65610, 65700, 65790, 65880, 65970, 66060, 66150, 66240, 66330, 66420, 66510, 66600, 66690, 66780, 66870, 66960, 67050, 67140, 67230, 67320, 67410, 67500, 67590, 67680, 67770, 67860, 67950, 68040, 68130, 68220, 68310, 68400, 68490, 68580, 68670, 68760, 68850, 68940, 69030, 69120, 69210, 69300, 69390, 69480, 69570, 69660, 69750, 69840, 69930, 70020, 70110, 70200, 70290, 70380, 70470, 70560, 70650, 70740, 70830, 70920, 71010, 71100, 71190, 71280, 71370, 71460, 71550, 71640, 71730, 71820, 71910, 72000, 72090, 72180, 72270, 72360, 72450, 72540, 72630, 72720, 72810, 72900, 72990, 73080, 73170, 73260, 73350, 73440, 73530, 73620, 73710, 73800, 73890, 73980, 74070, 74160, 74250, 74340, 74430, 74520, 74610, 74700, 74790, 74880, 74970, 75060, 75150, 75240, 75330, 75420, 75510, 75600, 75690, 75780, 75870, 75960, 76050, 76140, 76230, 76320, 76410, 76500, 76590, 76680, 76770, 76860, 76950, 77040, 77130, 77220, 77310, 77400, 77490, 77580, 77670, 77760, 77850, 77940, 78030, 78120, 78210, 78300, 78390, 78480, 78570, 78660, 78750, 78840, 78930, 79020, 79110, 79200, 79290, 79380, 79470, 79560, 79650, 79740, 79830, 79920, 80010, 80100, 80190, 80280, 80370, 80460, 80550, 80640, 80730, 80820, 80910, 81000, 81090, 81180, 81270, 81360, 81450, 81540, 81630, 81720, 81810, 81900, 81990, 82080, 82170, 82260, 82350, 82440, 82530, 82620, 82710, 82800, 82890, 82980, 83070, 83160, 83250, 83340, 83430, 83520, 83610, 83700, 83790, 83880, 83970, 84060, 84150, 84240, 84330, 84420, 84510, 84600, 84690, 84780, 84870, 84960, 85050, 85140, 85230, 85320, 85410, 85500, 85590, 85680, 85770, 85860, 85950, 86040, 86130, 86220, 86310, 86400, 86490, 86580, 86670, 86760, 86850, 86940, 87030, 87120, 87210, 87300, 87390, 87480, 87570, 87660, 87750, 87840, 87930, 88020, 88110, 88200, 88290, 88380, 88470, 88560, 88650, 88740, 88830, 88920, 89010, 89100, 89190, 89280, 89370, 89460, 89550, 89640, 89730, 89820, 89910, 90000, 90090, 90180, 90270, 90360, 90450, 90540, 90630, 90720, 90810, 90900, 90990, 91080, 91170, 91260, 91350, 91440, 91530, 91620, 91710, 91800, 91890, 91980, 92070, 92160, 92250, 92340, 92430, 92520, 92610, 92700, 92790, 92880, 92970, 93060, 93150, 93240, 93330, 93420, 93510, 93600, 93690, 93780, 93870, 93960, 94050, 94140, 94230, 94320, 94410, 94500, 94590, 94680, 94770, 94860, 94950, 95040, 95130, 95220, 95310, 95400, 95490, 95580, 95670, 95760, 95850, 95940, 96030, 96120, 96210, 96300, 96390, 96480, 96570, 96660, 96750, 96840, 96930, 97020, 97110, 97200, 97290, 97380, 97470, 97560, 97650, 97740, 97830, 97920, 98010, 98100, 98190, 98280, 98370, 98460, 98550, 98640, 98730, 98820, 98910, 99000, 99090, 99180, 99270, 99360, 99450, 99540, 99630, 99720, 99810, 99900, 99990

There is a total of 1111 numbers (up to 100000) that are divisible by 90.
The sum of these numbers is 55594440.
The arithmetic mean of these numbers is 50040.

How to find the numbers divisible by 90?

Finding all the numbers that can be divided by 90 is essentially the same as searching for the multiples of 90: if a number N is a multiple of 90, then 90 is a divisor of N.

Indeed, if we assume that N is a multiple of 90, this means there exists an integer k such that:

$k \times 90 = N$

Conversely, the result of N divided by 90 is this same integer k (without any remainder):

$k = \frac{N}{90}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 90 (we can keep multiplying it by increasingly larger integers, without ever reaching the end).

However, in this instance, we've chosen to set an arbitrary limit (specifically, the multiples of 90 less than 100000):

1 × 90 = 90
2 × 90 = 180
3 × 90 = 270
...
1110 × 90 = 99900
1111 × 90 = 99990