What are the numbers divisible by 120?
120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200, 1320, 1440, 1560, 1680, 1800, 1920, 2040, 2160, 2280, 2400, 2520, 2640, 2760, 2880, 3000, 3120, 3240, 3360, 3480, 3600, 3720, 3840, 3960, 4080, 4200, 4320, 4440, 4560, 4680, 4800, 4920, 5040, 5160, 5280, 5400, 5520, 5640, 5760, 5880, 6000, 6120, 6240, 6360, 6480, 6600, 6720, 6840, 6960, 7080, 7200, 7320, 7440, 7560, 7680, 7800, 7920, 8040, 8160, 8280, 8400, 8520, 8640, 8760, 8880, 9000, 9120, 9240, 9360, 9480, 9600, 9720, 9840, 9960, 10080, 10200, 10320, 10440, 10560, 10680, 10800, 10920, 11040, 11160, 11280, 11400, 11520, 11640, 11760, 11880, 12000, 12120, 12240, 12360, 12480, 12600, 12720, 12840, 12960, 13080, 13200, 13320, 13440, 13560, 13680, 13800, 13920, 14040, 14160, 14280, 14400, 14520, 14640, 14760, 14880, 15000, 15120, 15240, 15360, 15480, 15600, 15720, 15840, 15960, 16080, 16200, 16320, 16440, 16560, 16680, 16800, 16920, 17040, 17160, 17280, 17400, 17520, 17640, 17760, 17880, 18000, 18120, 18240, 18360, 18480, 18600, 18720, 18840, 18960, 19080, 19200, 19320, 19440, 19560, 19680, 19800, 19920, 20040, 20160, 20280, 20400, 20520, 20640, 20760, 20880, 21000, 21120, 21240, 21360, 21480, 21600, 21720, 21840, 21960, 22080, 22200, 22320, 22440, 22560, 22680, 22800, 22920, 23040, 23160, 23280, 23400, 23520, 23640, 23760, 23880, 24000, 24120, 24240, 24360, 24480, 24600, 24720, 24840, 24960, 25080, 25200, 25320, 25440, 25560, 25680, 25800, 25920, 26040, 26160, 26280, 26400, 26520, 26640, 26760, 26880, 27000, 27120, 27240, 27360, 27480, 27600, 27720, 27840, 27960, 28080, 28200, 28320, 28440, 28560, 28680, 28800, 28920, 29040, 29160, 29280, 29400, 29520, 29640, 29760, 29880, 30000, 30120, 30240, 30360, 30480, 30600, 30720, 30840, 30960, 31080, 31200, 31320, 31440, 31560, 31680, 31800, 31920, 32040, 32160, 32280, 32400, 32520, 32640, 32760, 32880, 33000, 33120, 33240, 33360, 33480, 33600, 33720, 33840, 33960, 34080, 34200, 34320, 34440, 34560, 34680, 34800, 34920, 35040, 35160, 35280, 35400, 35520, 35640, 35760, 35880, 36000, 36120, 36240, 36360, 36480, 36600, 36720, 36840, 36960, 37080, 37200, 37320, 37440, 37560, 37680, 37800, 37920, 38040, 38160, 38280, 38400, 38520, 38640, 38760, 38880, 39000, 39120, 39240, 39360, 39480, 39600, 39720, 39840, 39960, 40080, 40200, 40320, 40440, 40560, 40680, 40800, 40920, 41040, 41160, 41280, 41400, 41520, 41640, 41760, 41880, 42000, 42120, 42240, 42360, 42480, 42600, 42720, 42840, 42960, 43080, 43200, 43320, 43440, 43560, 43680, 43800, 43920, 44040, 44160, 44280, 44400, 44520, 44640, 44760, 44880, 45000, 45120, 45240, 45360, 45480, 45600, 45720, 45840, 45960, 46080, 46200, 46320, 46440, 46560, 46680, 46800, 46920, 47040, 47160, 47280, 47400, 47520, 47640, 47760, 47880, 48000, 48120, 48240, 48360, 48480, 48600, 48720, 48840, 48960, 49080, 49200, 49320, 49440, 49560, 49680, 49800, 49920, 50040, 50160, 50280, 50400, 50520, 50640, 50760, 50880, 51000, 51120, 51240, 51360, 51480, 51600, 51720, 51840, 51960, 52080, 52200, 52320, 52440, 52560, 52680, 52800, 52920, 53040, 53160, 53280, 53400, 53520, 53640, 53760, 53880, 54000, 54120, 54240, 54360, 54480, 54600, 54720, 54840, 54960, 55080, 55200, 55320, 55440, 55560, 55680, 55800, 55920, 56040, 56160, 56280, 56400, 56520, 56640, 56760, 56880, 57000, 57120, 57240, 57360, 57480, 57600, 57720, 57840, 57960, 58080, 58200, 58320, 58440, 58560, 58680, 58800, 58920, 59040, 59160, 59280, 59400, 59520, 59640, 59760, 59880, 60000, 60120, 60240, 60360, 60480, 60600, 60720, 60840, 60960, 61080, 61200, 61320, 61440, 61560, 61680, 61800, 61920, 62040, 62160, 62280, 62400, 62520, 62640, 62760, 62880, 63000, 63120, 63240, 63360, 63480, 63600, 63720, 63840, 63960, 64080, 64200, 64320, 64440, 64560, 64680, 64800, 64920, 65040, 65160, 65280, 65400, 65520, 65640, 65760, 65880, 66000, 66120, 66240, 66360, 66480, 66600, 66720, 66840, 66960, 67080, 67200, 67320, 67440, 67560, 67680, 67800, 67920, 68040, 68160, 68280, 68400, 68520, 68640, 68760, 68880, 69000, 69120, 69240, 69360, 69480, 69600, 69720, 69840, 69960, 70080, 70200, 70320, 70440, 70560, 70680, 70800, 70920, 71040, 71160, 71280, 71400, 71520, 71640, 71760, 71880, 72000, 72120, 72240, 72360, 72480, 72600, 72720, 72840, 72960, 73080, 73200, 73320, 73440, 73560, 73680, 73800, 73920, 74040, 74160, 74280, 74400, 74520, 74640, 74760, 74880, 75000, 75120, 75240, 75360, 75480, 75600, 75720, 75840, 75960, 76080, 76200, 76320, 76440, 76560, 76680, 76800, 76920, 77040, 77160, 77280, 77400, 77520, 77640, 77760, 77880, 78000, 78120, 78240, 78360, 78480, 78600, 78720, 78840, 78960, 79080, 79200, 79320, 79440, 79560, 79680, 79800, 79920, 80040, 80160, 80280, 80400, 80520, 80640, 80760, 80880, 81000, 81120, 81240, 81360, 81480, 81600, 81720, 81840, 81960, 82080, 82200, 82320, 82440, 82560, 82680, 82800, 82920, 83040, 83160, 83280, 83400, 83520, 83640, 83760, 83880, 84000, 84120, 84240, 84360, 84480, 84600, 84720, 84840, 84960, 85080, 85200, 85320, 85440, 85560, 85680, 85800, 85920, 86040, 86160, 86280, 86400, 86520, 86640, 86760, 86880, 87000, 87120, 87240, 87360, 87480, 87600, 87720, 87840, 87960, 88080, 88200, 88320, 88440, 88560, 88680, 88800, 88920, 89040, 89160, 89280, 89400, 89520, 89640, 89760, 89880, 90000, 90120, 90240, 90360, 90480, 90600, 90720, 90840, 90960, 91080, 91200, 91320, 91440, 91560, 91680, 91800, 91920, 92040, 92160, 92280, 92400, 92520, 92640, 92760, 92880, 93000, 93120, 93240, 93360, 93480, 93600, 93720, 93840, 93960, 94080, 94200, 94320, 94440, 94560, 94680, 94800, 94920, 95040, 95160, 95280, 95400, 95520, 95640, 95760, 95880, 96000, 96120, 96240, 96360, 96480, 96600, 96720, 96840, 96960, 97080, 97200, 97320, 97440, 97560, 97680, 97800, 97920, 98040, 98160, 98280, 98400, 98520, 98640, 98760, 98880, 99000, 99120, 99240, 99360, 99480, 99600, 99720, 99840, 99960
- There is a total of 833 numbers (up to 100000) that are divisible by 120.
- The sum of these numbers is 41683320.
- The arithmetic mean of these numbers is 50040.
How to find the numbers divisible by 120?
Finding all the numbers that can be divided by 120 is essentially the same as searching for the multiples of 120: if a number N is a multiple of 120, then 120 is a divisor of N.
Indeed, if we assume that N is a multiple of 120, this means there exists an integer k such that:
Conversely, the result of N divided by 120 is this same integer k (without any remainder):
From this we can see that, theoretically, there's an infinite quantity of multiples of 120 (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 120 less than 100000):
- 1 × 120 = 120
- 2 × 120 = 240
- 3 × 120 = 360
- ...
- 832 × 120 = 99840
- 833 × 120 = 99960