What are the numbers divisible by 135?
135, 270, 405, 540, 675, 810, 945, 1080, 1215, 1350, 1485, 1620, 1755, 1890, 2025, 2160, 2295, 2430, 2565, 2700, 2835, 2970, 3105, 3240, 3375, 3510, 3645, 3780, 3915, 4050, 4185, 4320, 4455, 4590, 4725, 4860, 4995, 5130, 5265, 5400, 5535, 5670, 5805, 5940, 6075, 6210, 6345, 6480, 6615, 6750, 6885, 7020, 7155, 7290, 7425, 7560, 7695, 7830, 7965, 8100, 8235, 8370, 8505, 8640, 8775, 8910, 9045, 9180, 9315, 9450, 9585, 9720, 9855, 9990, 10125, 10260, 10395, 10530, 10665, 10800, 10935, 11070, 11205, 11340, 11475, 11610, 11745, 11880, 12015, 12150, 12285, 12420, 12555, 12690, 12825, 12960, 13095, 13230, 13365, 13500, 13635, 13770, 13905, 14040, 14175, 14310, 14445, 14580, 14715, 14850, 14985, 15120, 15255, 15390, 15525, 15660, 15795, 15930, 16065, 16200, 16335, 16470, 16605, 16740, 16875, 17010, 17145, 17280, 17415, 17550, 17685, 17820, 17955, 18090, 18225, 18360, 18495, 18630, 18765, 18900, 19035, 19170, 19305, 19440, 19575, 19710, 19845, 19980, 20115, 20250, 20385, 20520, 20655, 20790, 20925, 21060, 21195, 21330, 21465, 21600, 21735, 21870, 22005, 22140, 22275, 22410, 22545, 22680, 22815, 22950, 23085, 23220, 23355, 23490, 23625, 23760, 23895, 24030, 24165, 24300, 24435, 24570, 24705, 24840, 24975, 25110, 25245, 25380, 25515, 25650, 25785, 25920, 26055, 26190, 26325, 26460, 26595, 26730, 26865, 27000, 27135, 27270, 27405, 27540, 27675, 27810, 27945, 28080, 28215, 28350, 28485, 28620, 28755, 28890, 29025, 29160, 29295, 29430, 29565, 29700, 29835, 29970, 30105, 30240, 30375, 30510, 30645, 30780, 30915, 31050, 31185, 31320, 31455, 31590, 31725, 31860, 31995, 32130, 32265, 32400, 32535, 32670, 32805, 32940, 33075, 33210, 33345, 33480, 33615, 33750, 33885, 34020, 34155, 34290, 34425, 34560, 34695, 34830, 34965, 35100, 35235, 35370, 35505, 35640, 35775, 35910, 36045, 36180, 36315, 36450, 36585, 36720, 36855, 36990, 37125, 37260, 37395, 37530, 37665, 37800, 37935, 38070, 38205, 38340, 38475, 38610, 38745, 38880, 39015, 39150, 39285, 39420, 39555, 39690, 39825, 39960, 40095, 40230, 40365, 40500, 40635, 40770, 40905, 41040, 41175, 41310, 41445, 41580, 41715, 41850, 41985, 42120, 42255, 42390, 42525, 42660, 42795, 42930, 43065, 43200, 43335, 43470, 43605, 43740, 43875, 44010, 44145, 44280, 44415, 44550, 44685, 44820, 44955, 45090, 45225, 45360, 45495, 45630, 45765, 45900, 46035, 46170, 46305, 46440, 46575, 46710, 46845, 46980, 47115, 47250, 47385, 47520, 47655, 47790, 47925, 48060, 48195, 48330, 48465, 48600, 48735, 48870, 49005, 49140, 49275, 49410, 49545, 49680, 49815, 49950, 50085, 50220, 50355, 50490, 50625, 50760, 50895, 51030, 51165, 51300, 51435, 51570, 51705, 51840, 51975, 52110, 52245, 52380, 52515, 52650, 52785, 52920, 53055, 53190, 53325, 53460, 53595, 53730, 53865, 54000, 54135, 54270, 54405, 54540, 54675, 54810, 54945, 55080, 55215, 55350, 55485, 55620, 55755, 55890, 56025, 56160, 56295, 56430, 56565, 56700, 56835, 56970, 57105, 57240, 57375, 57510, 57645, 57780, 57915, 58050, 58185, 58320, 58455, 58590, 58725, 58860, 58995, 59130, 59265, 59400, 59535, 59670, 59805, 59940, 60075, 60210, 60345, 60480, 60615, 60750, 60885, 61020, 61155, 61290, 61425, 61560, 61695, 61830, 61965, 62100, 62235, 62370, 62505, 62640, 62775, 62910, 63045, 63180, 63315, 63450, 63585, 63720, 63855, 63990, 64125, 64260, 64395, 64530, 64665, 64800, 64935, 65070, 65205, 65340, 65475, 65610, 65745, 65880, 66015, 66150, 66285, 66420, 66555, 66690, 66825, 66960, 67095, 67230, 67365, 67500, 67635, 67770, 67905, 68040, 68175, 68310, 68445, 68580, 68715, 68850, 68985, 69120, 69255, 69390, 69525, 69660, 69795, 69930, 70065, 70200, 70335, 70470, 70605, 70740, 70875, 71010, 71145, 71280, 71415, 71550, 71685, 71820, 71955, 72090, 72225, 72360, 72495, 72630, 72765, 72900, 73035, 73170, 73305, 73440, 73575, 73710, 73845, 73980, 74115, 74250, 74385, 74520, 74655, 74790, 74925, 75060, 75195, 75330, 75465, 75600, 75735, 75870, 76005, 76140, 76275, 76410, 76545, 76680, 76815, 76950, 77085, 77220, 77355, 77490, 77625, 77760, 77895, 78030, 78165, 78300, 78435, 78570, 78705, 78840, 78975, 79110, 79245, 79380, 79515, 79650, 79785, 79920, 80055, 80190, 80325, 80460, 80595, 80730, 80865, 81000, 81135, 81270, 81405, 81540, 81675, 81810, 81945, 82080, 82215, 82350, 82485, 82620, 82755, 82890, 83025, 83160, 83295, 83430, 83565, 83700, 83835, 83970, 84105, 84240, 84375, 84510, 84645, 84780, 84915, 85050, 85185, 85320, 85455, 85590, 85725, 85860, 85995, 86130, 86265, 86400, 86535, 86670, 86805, 86940, 87075, 87210, 87345, 87480, 87615, 87750, 87885, 88020, 88155, 88290, 88425, 88560, 88695, 88830, 88965, 89100, 89235, 89370, 89505, 89640, 89775, 89910, 90045, 90180, 90315, 90450, 90585, 90720, 90855, 90990, 91125, 91260, 91395, 91530, 91665, 91800, 91935, 92070, 92205, 92340, 92475, 92610, 92745, 92880, 93015, 93150, 93285, 93420, 93555, 93690, 93825, 93960, 94095, 94230, 94365, 94500, 94635, 94770, 94905, 95040, 95175, 95310, 95445, 95580, 95715, 95850, 95985, 96120, 96255, 96390, 96525, 96660, 96795, 96930, 97065, 97200, 97335, 97470, 97605, 97740, 97875, 98010, 98145, 98280, 98415, 98550, 98685, 98820, 98955, 99090, 99225, 99360, 99495, 99630, 99765, 99900
- There is a total of 740 numbers (up to 100000) that are divisible by 135.
- The sum of these numbers is 37012950.
- The arithmetic mean of these numbers is 50017.5.
How to find the numbers divisible by 135?
Finding all the numbers that can be divided by 135 is essentially the same as searching for the multiples of 135: if a number N is a multiple of 135, then 135 is a divisor of N.
Indeed, if we assume that N is a multiple of 135, this means there exists an integer k such that:
Conversely, the result of N divided by 135 is this same integer k (without any remainder):
From this we can see that, theoretically, there's an infinite quantity of multiples of 135 (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 135 less than 100000):
- 1 × 135 = 135
- 2 × 135 = 270
- 3 × 135 = 405
- ...
- 739 × 135 = 99765
- 740 × 135 = 99900