What are the numbers divisible by 72?
72, 144, 216, 288, 360, 432, 504, 576, 648, 720, 792, 864, 936, 1008, 1080, 1152, 1224, 1296, 1368, 1440, 1512, 1584, 1656, 1728, 1800, 1872, 1944, 2016, 2088, 2160, 2232, 2304, 2376, 2448, 2520, 2592, 2664, 2736, 2808, 2880, 2952, 3024, 3096, 3168, 3240, 3312, 3384, 3456, 3528, 3600, 3672, 3744, 3816, 3888, 3960, 4032, 4104, 4176, 4248, 4320, 4392, 4464, 4536, 4608, 4680, 4752, 4824, 4896, 4968, 5040, 5112, 5184, 5256, 5328, 5400, 5472, 5544, 5616, 5688, 5760, 5832, 5904, 5976, 6048, 6120, 6192, 6264, 6336, 6408, 6480, 6552, 6624, 6696, 6768, 6840, 6912, 6984, 7056, 7128, 7200, 7272, 7344, 7416, 7488, 7560, 7632, 7704, 7776, 7848, 7920, 7992, 8064, 8136, 8208, 8280, 8352, 8424, 8496, 8568, 8640, 8712, 8784, 8856, 8928, 9000, 9072, 9144, 9216, 9288, 9360, 9432, 9504, 9576, 9648, 9720, 9792, 9864, 9936, 10008, 10080, 10152, 10224, 10296, 10368, 10440, 10512, 10584, 10656, 10728, 10800, 10872, 10944, 11016, 11088, 11160, 11232, 11304, 11376, 11448, 11520, 11592, 11664, 11736, 11808, 11880, 11952, 12024, 12096, 12168, 12240, 12312, 12384, 12456, 12528, 12600, 12672, 12744, 12816, 12888, 12960, 13032, 13104, 13176, 13248, 13320, 13392, 13464, 13536, 13608, 13680, 13752, 13824, 13896, 13968, 14040, 14112, 14184, 14256, 14328, 14400, 14472, 14544, 14616, 14688, 14760, 14832, 14904, 14976, 15048, 15120, 15192, 15264, 15336, 15408, 15480, 15552, 15624, 15696, 15768, 15840, 15912, 15984, 16056, 16128, 16200, 16272, 16344, 16416, 16488, 16560, 16632, 16704, 16776, 16848, 16920, 16992, 17064, 17136, 17208, 17280, 17352, 17424, 17496, 17568, 17640, 17712, 17784, 17856, 17928, 18000, 18072, 18144, 18216, 18288, 18360, 18432, 18504, 18576, 18648, 18720, 18792, 18864, 18936, 19008, 19080, 19152, 19224, 19296, 19368, 19440, 19512, 19584, 19656, 19728, 19800, 19872, 19944, 20016, 20088, 20160, 20232, 20304, 20376, 20448, 20520, 20592, 20664, 20736, 20808, 20880, 20952, 21024, 21096, 21168, 21240, 21312, 21384, 21456, 21528, 21600, 21672, 21744, 21816, 21888, 21960, 22032, 22104, 22176, 22248, 22320, 22392, 22464, 22536, 22608, 22680, 22752, 22824, 22896, 22968, 23040, 23112, 23184, 23256, 23328, 23400, 23472, 23544, 23616, 23688, 23760, 23832, 23904, 23976, 24048, 24120, 24192, 24264, 24336, 24408, 24480, 24552, 24624, 24696, 24768, 24840, 24912, 24984, 25056, 25128, 25200, 25272, 25344, 25416, 25488, 25560, 25632, 25704, 25776, 25848, 25920, 25992, 26064, 26136, 26208, 26280, 26352, 26424, 26496, 26568, 26640, 26712, 26784, 26856, 26928, 27000, 27072, 27144, 27216, 27288, 27360, 27432, 27504, 27576, 27648, 27720, 27792, 27864, 27936, 28008, 28080, 28152, 28224, 28296, 28368, 28440, 28512, 28584, 28656, 28728, 28800, 28872, 28944, 29016, 29088, 29160, 29232, 29304, 29376, 29448, 29520, 29592, 29664, 29736, 29808, 29880, 29952, 30024, 30096, 30168, 30240, 30312, 30384, 30456, 30528, 30600, 30672, 30744, 30816, 30888, 30960, 31032, 31104, 31176, 31248, 31320, 31392, 31464, 31536, 31608, 31680, 31752, 31824, 31896, 31968, 32040, 32112, 32184, 32256, 32328, 32400, 32472, 32544, 32616, 32688, 32760, 32832, 32904, 32976, 33048, 33120, 33192, 33264, 33336, 33408, 33480, 33552, 33624, 33696, 33768, 33840, 33912, 33984, 34056, 34128, 34200, 34272, 34344, 34416, 34488, 34560, 34632, 34704, 34776, 34848, 34920, 34992, 35064, 35136, 35208, 35280, 35352, 35424, 35496, 35568, 35640, 35712, 35784, 35856, 35928, 36000, 36072, 36144, 36216, 36288, 36360, 36432, 36504, 36576, 36648, 36720, 36792, 36864, 36936, 37008, 37080, 37152, 37224, 37296, 37368, 37440, 37512, 37584, 37656, 37728, 37800, 37872, 37944, 38016, 38088, 38160, 38232, 38304, 38376, 38448, 38520, 38592, 38664, 38736, 38808, 38880, 38952, 39024, 39096, 39168, 39240, 39312, 39384, 39456, 39528, 39600, 39672, 39744, 39816, 39888, 39960, 40032, 40104, 40176, 40248, 40320, 40392, 40464, 40536, 40608, 40680, 40752, 40824, 40896, 40968, 41040, 41112, 41184, 41256, 41328, 41400, 41472, 41544, 41616, 41688, 41760, 41832, 41904, 41976, 42048, 42120, 42192, 42264, 42336, 42408, 42480, 42552, 42624, 42696, 42768, 42840, 42912, 42984, 43056, 43128, 43200, 43272, 43344, 43416, 43488, 43560, 43632, 43704, 43776, 43848, 43920, 43992, 44064, 44136, 44208, 44280, 44352, 44424, 44496, 44568, 44640, 44712, 44784, 44856, 44928, 45000, 45072, 45144, 45216, 45288, 45360, 45432, 45504, 45576, 45648, 45720, 45792, 45864, 45936, 46008, 46080, 46152, 46224, 46296, 46368, 46440, 46512, 46584, 46656, 46728, 46800, 46872, 46944, 47016, 47088, 47160, 47232, 47304, 47376, 47448, 47520, 47592, 47664, 47736, 47808, 47880, 47952, 48024, 48096, 48168, 48240, 48312, 48384, 48456, 48528, 48600, 48672, 48744, 48816, 48888, 48960, 49032, 49104, 49176, 49248, 49320, 49392, 49464, 49536, 49608, 49680, 49752, 49824, 49896, 49968, 50040, 50112, 50184, 50256, 50328, 50400, 50472, 50544, 50616, 50688, 50760, 50832, 50904, 50976, 51048, 51120, 51192, 51264, 51336, 51408, 51480, 51552, 51624, 51696, 51768, 51840, 51912, 51984, 52056, 52128, 52200, 52272, 52344, 52416, 52488, 52560, 52632, 52704, 52776, 52848, 52920, 52992, 53064, 53136, 53208, 53280, 53352, 53424, 53496, 53568, 53640, 53712, 53784, 53856, 53928, 54000, 54072, 54144, 54216, 54288, 54360, 54432, 54504, 54576, 54648, 54720, 54792, 54864, 54936, 55008, 55080, 55152, 55224, 55296, 55368, 55440, 55512, 55584, 55656, 55728, 55800, 55872, 55944, 56016, 56088, 56160, 56232, 56304, 56376, 56448, 56520, 56592, 56664, 56736, 56808, 56880, 56952, 57024, 57096, 57168, 57240, 57312, 57384, 57456, 57528, 57600, 57672, 57744, 57816, 57888, 57960, 58032, 58104, 58176, 58248, 58320, 58392, 58464, 58536, 58608, 58680, 58752, 58824, 58896, 58968, 59040, 59112, 59184, 59256, 59328, 59400, 59472, 59544, 59616, 59688, 59760, 59832, 59904, 59976, 60048, 60120, 60192, 60264, 60336, 60408, 60480, 60552, 60624, 60696, 60768, 60840, 60912, 60984, 61056, 61128, 61200, 61272, 61344, 61416, 61488, 61560, 61632, 61704, 61776, 61848, 61920, 61992, 62064, 62136, 62208, 62280, 62352, 62424, 62496, 62568, 62640, 62712, 62784, 62856, 62928, 63000, 63072, 63144, 63216, 63288, 63360, 63432, 63504, 63576, 63648, 63720, 63792, 63864, 63936, 64008, 64080, 64152, 64224, 64296, 64368, 64440, 64512, 64584, 64656, 64728, 64800, 64872, 64944, 65016, 65088, 65160, 65232, 65304, 65376, 65448, 65520, 65592, 65664, 65736, 65808, 65880, 65952, 66024, 66096, 66168, 66240, 66312, 66384, 66456, 66528, 66600, 66672, 66744, 66816, 66888, 66960, 67032, 67104, 67176, 67248, 67320, 67392, 67464, 67536, 67608, 67680, 67752, 67824, 67896, 67968, 68040, 68112, 68184, 68256, 68328, 68400, 68472, 68544, 68616, 68688, 68760, 68832, 68904, 68976, 69048, 69120, 69192, 69264, 69336, 69408, 69480, 69552, 69624, 69696, 69768, 69840, 69912, 69984, 70056, 70128, 70200, 70272, 70344, 70416, 70488, 70560, 70632, 70704, 70776, 70848, 70920, 70992, 71064, 71136, 71208, 71280, 71352, 71424, 71496, 71568, 71640, 71712, 71784, 71856, 71928, 72000, 72072, 72144, 72216, 72288, 72360, 72432, 72504, 72576, 72648, 72720, 72792, 72864, 72936, 73008, 73080, 73152, 73224, 73296, 73368, 73440, 73512, 73584, 73656, 73728, 73800, 73872, 73944, 74016, 74088, 74160, 74232, 74304, 74376, 74448, 74520, 74592, 74664, 74736, 74808, 74880, 74952, 75024, 75096, 75168, 75240, 75312, 75384, 75456, 75528, 75600, 75672, 75744, 75816, 75888, 75960, 76032, 76104, 76176, 76248, 76320, 76392, 76464, 76536, 76608, 76680, 76752, 76824, 76896, 76968, 77040, 77112, 77184, 77256, 77328, 77400, 77472, 77544, 77616, 77688, 77760, 77832, 77904, 77976, 78048, 78120, 78192, 78264, 78336, 78408, 78480, 78552, 78624, 78696, 78768, 78840, 78912, 78984, 79056, 79128, 79200, 79272, 79344, 79416, 79488, 79560, 79632, 79704, 79776, 79848, 79920, 79992, 80064, 80136, 80208, 80280, 80352, 80424, 80496, 80568, 80640, 80712, 80784, 80856, 80928, 81000, 81072, 81144, 81216, 81288, 81360, 81432, 81504, 81576, 81648, 81720, 81792, 81864, 81936, 82008, 82080, 82152, 82224, 82296, 82368, 82440, 82512, 82584, 82656, 82728, 82800, 82872, 82944, 83016, 83088, 83160, 83232, 83304, 83376, 83448, 83520, 83592, 83664, 83736, 83808, 83880, 83952, 84024, 84096, 84168, 84240, 84312, 84384, 84456, 84528, 84600, 84672, 84744, 84816, 84888, 84960, 85032, 85104, 85176, 85248, 85320, 85392, 85464, 85536, 85608, 85680, 85752, 85824, 85896, 85968, 86040, 86112, 86184, 86256, 86328, 86400, 86472, 86544, 86616, 86688, 86760, 86832, 86904, 86976, 87048, 87120, 87192, 87264, 87336, 87408, 87480, 87552, 87624, 87696, 87768, 87840, 87912, 87984, 88056, 88128, 88200, 88272, 88344, 88416, 88488, 88560, 88632, 88704, 88776, 88848, 88920, 88992, 89064, 89136, 89208, 89280, 89352, 89424, 89496, 89568, 89640, 89712, 89784, 89856, 89928, 90000, 90072, 90144, 90216, 90288, 90360, 90432, 90504, 90576, 90648, 90720, 90792, 90864, 90936, 91008, 91080, 91152, 91224, 91296, 91368, 91440, 91512, 91584, 91656, 91728, 91800, 91872, 91944, 92016, 92088, 92160, 92232, 92304, 92376, 92448, 92520, 92592, 92664, 92736, 92808, 92880, 92952, 93024, 93096, 93168, 93240, 93312, 93384, 93456, 93528, 93600, 93672, 93744, 93816, 93888, 93960, 94032, 94104, 94176, 94248, 94320, 94392, 94464, 94536, 94608, 94680, 94752, 94824, 94896, 94968, 95040, 95112, 95184, 95256, 95328, 95400, 95472, 95544, 95616, 95688, 95760, 95832, 95904, 95976, 96048, 96120, 96192, 96264, 96336, 96408, 96480, 96552, 96624, 96696, 96768, 96840, 96912, 96984, 97056, 97128, 97200, 97272, 97344, 97416, 97488, 97560, 97632, 97704, 97776, 97848, 97920, 97992, 98064, 98136, 98208, 98280, 98352, 98424, 98496, 98568, 98640, 98712, 98784, 98856, 98928, 99000, 99072, 99144, 99216, 99288, 99360, 99432, 99504, 99576, 99648, 99720, 99792, 99864, 99936
- There is a total of 1388 numbers (up to 100000) that are divisible by 72.
- The sum of these numbers is 69405552.
- The arithmetic mean of these numbers is 50004.
How to find the numbers divisible by 72?
Finding all the numbers that can be divided by 72 is essentially the same as searching for the multiples of 72: if a number N is a multiple of 72, then 72 is a divisor of N.
Indeed, if we assume that N is a multiple of 72, this means there exists an integer k such that:
Conversely, the result of N divided by 72 is this same integer k (without any remainder):
From this we can see that, theoretically, there's an infinite quantity of multiples of 72 (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 72 less than 100000):
- 1 × 72 = 72
- 2 × 72 = 144
- 3 × 72 = 216
- ...
- 1387 × 72 = 99864
- 1388 × 72 = 99936