What are the numbers divisible by 68?
68, 136, 204, 272, 340, 408, 476, 544, 612, 680, 748, 816, 884, 952, 1020, 1088, 1156, 1224, 1292, 1360, 1428, 1496, 1564, 1632, 1700, 1768, 1836, 1904, 1972, 2040, 2108, 2176, 2244, 2312, 2380, 2448, 2516, 2584, 2652, 2720, 2788, 2856, 2924, 2992, 3060, 3128, 3196, 3264, 3332, 3400, 3468, 3536, 3604, 3672, 3740, 3808, 3876, 3944, 4012, 4080, 4148, 4216, 4284, 4352, 4420, 4488, 4556, 4624, 4692, 4760, 4828, 4896, 4964, 5032, 5100, 5168, 5236, 5304, 5372, 5440, 5508, 5576, 5644, 5712, 5780, 5848, 5916, 5984, 6052, 6120, 6188, 6256, 6324, 6392, 6460, 6528, 6596, 6664, 6732, 6800, 6868, 6936, 7004, 7072, 7140, 7208, 7276, 7344, 7412, 7480, 7548, 7616, 7684, 7752, 7820, 7888, 7956, 8024, 8092, 8160, 8228, 8296, 8364, 8432, 8500, 8568, 8636, 8704, 8772, 8840, 8908, 8976, 9044, 9112, 9180, 9248, 9316, 9384, 9452, 9520, 9588, 9656, 9724, 9792, 9860, 9928, 9996, 10064, 10132, 10200, 10268, 10336, 10404, 10472, 10540, 10608, 10676, 10744, 10812, 10880, 10948, 11016, 11084, 11152, 11220, 11288, 11356, 11424, 11492, 11560, 11628, 11696, 11764, 11832, 11900, 11968, 12036, 12104, 12172, 12240, 12308, 12376, 12444, 12512, 12580, 12648, 12716, 12784, 12852, 12920, 12988, 13056, 13124, 13192, 13260, 13328, 13396, 13464, 13532, 13600, 13668, 13736, 13804, 13872, 13940, 14008, 14076, 14144, 14212, 14280, 14348, 14416, 14484, 14552, 14620, 14688, 14756, 14824, 14892, 14960, 15028, 15096, 15164, 15232, 15300, 15368, 15436, 15504, 15572, 15640, 15708, 15776, 15844, 15912, 15980, 16048, 16116, 16184, 16252, 16320, 16388, 16456, 16524, 16592, 16660, 16728, 16796, 16864, 16932, 17000, 17068, 17136, 17204, 17272, 17340, 17408, 17476, 17544, 17612, 17680, 17748, 17816, 17884, 17952, 18020, 18088, 18156, 18224, 18292, 18360, 18428, 18496, 18564, 18632, 18700, 18768, 18836, 18904, 18972, 19040, 19108, 19176, 19244, 19312, 19380, 19448, 19516, 19584, 19652, 19720, 19788, 19856, 19924, 19992, 20060, 20128, 20196, 20264, 20332, 20400, 20468, 20536, 20604, 20672, 20740, 20808, 20876, 20944, 21012, 21080, 21148, 21216, 21284, 21352, 21420, 21488, 21556, 21624, 21692, 21760, 21828, 21896, 21964, 22032, 22100, 22168, 22236, 22304, 22372, 22440, 22508, 22576, 22644, 22712, 22780, 22848, 22916, 22984, 23052, 23120, 23188, 23256, 23324, 23392, 23460, 23528, 23596, 23664, 23732, 23800, 23868, 23936, 24004, 24072, 24140, 24208, 24276, 24344, 24412, 24480, 24548, 24616, 24684, 24752, 24820, 24888, 24956, 25024, 25092, 25160, 25228, 25296, 25364, 25432, 25500, 25568, 25636, 25704, 25772, 25840, 25908, 25976, 26044, 26112, 26180, 26248, 26316, 26384, 26452, 26520, 26588, 26656, 26724, 26792, 26860, 26928, 26996, 27064, 27132, 27200, 27268, 27336, 27404, 27472, 27540, 27608, 27676, 27744, 27812, 27880, 27948, 28016, 28084, 28152, 28220, 28288, 28356, 28424, 28492, 28560, 28628, 28696, 28764, 28832, 28900, 28968, 29036, 29104, 29172, 29240, 29308, 29376, 29444, 29512, 29580, 29648, 29716, 29784, 29852, 29920, 29988, 30056, 30124, 30192, 30260, 30328, 30396, 30464, 30532, 30600, 30668, 30736, 30804, 30872, 30940, 31008, 31076, 31144, 31212, 31280, 31348, 31416, 31484, 31552, 31620, 31688, 31756, 31824, 31892, 31960, 32028, 32096, 32164, 32232, 32300, 32368, 32436, 32504, 32572, 32640, 32708, 32776, 32844, 32912, 32980, 33048, 33116, 33184, 33252, 33320, 33388, 33456, 33524, 33592, 33660, 33728, 33796, 33864, 33932, 34000, 34068, 34136, 34204, 34272, 34340, 34408, 34476, 34544, 34612, 34680, 34748, 34816, 34884, 34952, 35020, 35088, 35156, 35224, 35292, 35360, 35428, 35496, 35564, 35632, 35700, 35768, 35836, 35904, 35972, 36040, 36108, 36176, 36244, 36312, 36380, 36448, 36516, 36584, 36652, 36720, 36788, 36856, 36924, 36992, 37060, 37128, 37196, 37264, 37332, 37400, 37468, 37536, 37604, 37672, 37740, 37808, 37876, 37944, 38012, 38080, 38148, 38216, 38284, 38352, 38420, 38488, 38556, 38624, 38692, 38760, 38828, 38896, 38964, 39032, 39100, 39168, 39236, 39304, 39372, 39440, 39508, 39576, 39644, 39712, 39780, 39848, 39916, 39984, 40052, 40120, 40188, 40256, 40324, 40392, 40460, 40528, 40596, 40664, 40732, 40800, 40868, 40936, 41004, 41072, 41140, 41208, 41276, 41344, 41412, 41480, 41548, 41616, 41684, 41752, 41820, 41888, 41956, 42024, 42092, 42160, 42228, 42296, 42364, 42432, 42500, 42568, 42636, 42704, 42772, 42840, 42908, 42976, 43044, 43112, 43180, 43248, 43316, 43384, 43452, 43520, 43588, 43656, 43724, 43792, 43860, 43928, 43996, 44064, 44132, 44200, 44268, 44336, 44404, 44472, 44540, 44608, 44676, 44744, 44812, 44880, 44948, 45016, 45084, 45152, 45220, 45288, 45356, 45424, 45492, 45560, 45628, 45696, 45764, 45832, 45900, 45968, 46036, 46104, 46172, 46240, 46308, 46376, 46444, 46512, 46580, 46648, 46716, 46784, 46852, 46920, 46988, 47056, 47124, 47192, 47260, 47328, 47396, 47464, 47532, 47600, 47668, 47736, 47804, 47872, 47940, 48008, 48076, 48144, 48212, 48280, 48348, 48416, 48484, 48552, 48620, 48688, 48756, 48824, 48892, 48960, 49028, 49096, 49164, 49232, 49300, 49368, 49436, 49504, 49572, 49640, 49708, 49776, 49844, 49912, 49980, 50048, 50116, 50184, 50252, 50320, 50388, 50456, 50524, 50592, 50660, 50728, 50796, 50864, 50932, 51000, 51068, 51136, 51204, 51272, 51340, 51408, 51476, 51544, 51612, 51680, 51748, 51816, 51884, 51952, 52020, 52088, 52156, 52224, 52292, 52360, 52428, 52496, 52564, 52632, 52700, 52768, 52836, 52904, 52972, 53040, 53108, 53176, 53244, 53312, 53380, 53448, 53516, 53584, 53652, 53720, 53788, 53856, 53924, 53992, 54060, 54128, 54196, 54264, 54332, 54400, 54468, 54536, 54604, 54672, 54740, 54808, 54876, 54944, 55012, 55080, 55148, 55216, 55284, 55352, 55420, 55488, 55556, 55624, 55692, 55760, 55828, 55896, 55964, 56032, 56100, 56168, 56236, 56304, 56372, 56440, 56508, 56576, 56644, 56712, 56780, 56848, 56916, 56984, 57052, 57120, 57188, 57256, 57324, 57392, 57460, 57528, 57596, 57664, 57732, 57800, 57868, 57936, 58004, 58072, 58140, 58208, 58276, 58344, 58412, 58480, 58548, 58616, 58684, 58752, 58820, 58888, 58956, 59024, 59092, 59160, 59228, 59296, 59364, 59432, 59500, 59568, 59636, 59704, 59772, 59840, 59908, 59976, 60044, 60112, 60180, 60248, 60316, 60384, 60452, 60520, 60588, 60656, 60724, 60792, 60860, 60928, 60996, 61064, 61132, 61200, 61268, 61336, 61404, 61472, 61540, 61608, 61676, 61744, 61812, 61880, 61948, 62016, 62084, 62152, 62220, 62288, 62356, 62424, 62492, 62560, 62628, 62696, 62764, 62832, 62900, 62968, 63036, 63104, 63172, 63240, 63308, 63376, 63444, 63512, 63580, 63648, 63716, 63784, 63852, 63920, 63988, 64056, 64124, 64192, 64260, 64328, 64396, 64464, 64532, 64600, 64668, 64736, 64804, 64872, 64940, 65008, 65076, 65144, 65212, 65280, 65348, 65416, 65484, 65552, 65620, 65688, 65756, 65824, 65892, 65960, 66028, 66096, 66164, 66232, 66300, 66368, 66436, 66504, 66572, 66640, 66708, 66776, 66844, 66912, 66980, 67048, 67116, 67184, 67252, 67320, 67388, 67456, 67524, 67592, 67660, 67728, 67796, 67864, 67932, 68000, 68068, 68136, 68204, 68272, 68340, 68408, 68476, 68544, 68612, 68680, 68748, 68816, 68884, 68952, 69020, 69088, 69156, 69224, 69292, 69360, 69428, 69496, 69564, 69632, 69700, 69768, 69836, 69904, 69972, 70040, 70108, 70176, 70244, 70312, 70380, 70448, 70516, 70584, 70652, 70720, 70788, 70856, 70924, 70992, 71060, 71128, 71196, 71264, 71332, 71400, 71468, 71536, 71604, 71672, 71740, 71808, 71876, 71944, 72012, 72080, 72148, 72216, 72284, 72352, 72420, 72488, 72556, 72624, 72692, 72760, 72828, 72896, 72964, 73032, 73100, 73168, 73236, 73304, 73372, 73440, 73508, 73576, 73644, 73712, 73780, 73848, 73916, 73984, 74052, 74120, 74188, 74256, 74324, 74392, 74460, 74528, 74596, 74664, 74732, 74800, 74868, 74936, 75004, 75072, 75140, 75208, 75276, 75344, 75412, 75480, 75548, 75616, 75684, 75752, 75820, 75888, 75956, 76024, 76092, 76160, 76228, 76296, 76364, 76432, 76500, 76568, 76636, 76704, 76772, 76840, 76908, 76976, 77044, 77112, 77180, 77248, 77316, 77384, 77452, 77520, 77588, 77656, 77724, 77792, 77860, 77928, 77996, 78064, 78132, 78200, 78268, 78336, 78404, 78472, 78540, 78608, 78676, 78744, 78812, 78880, 78948, 79016, 79084, 79152, 79220, 79288, 79356, 79424, 79492, 79560, 79628, 79696, 79764, 79832, 79900, 79968, 80036, 80104, 80172, 80240, 80308, 80376, 80444, 80512, 80580, 80648, 80716, 80784, 80852, 80920, 80988, 81056, 81124, 81192, 81260, 81328, 81396, 81464, 81532, 81600, 81668, 81736, 81804, 81872, 81940, 82008, 82076, 82144, 82212, 82280, 82348, 82416, 82484, 82552, 82620, 82688, 82756, 82824, 82892, 82960, 83028, 83096, 83164, 83232, 83300, 83368, 83436, 83504, 83572, 83640, 83708, 83776, 83844, 83912, 83980, 84048, 84116, 84184, 84252, 84320, 84388, 84456, 84524, 84592, 84660, 84728, 84796, 84864, 84932, 85000, 85068, 85136, 85204, 85272, 85340, 85408, 85476, 85544, 85612, 85680, 85748, 85816, 85884, 85952, 86020, 86088, 86156, 86224, 86292, 86360, 86428, 86496, 86564, 86632, 86700, 86768, 86836, 86904, 86972, 87040, 87108, 87176, 87244, 87312, 87380, 87448, 87516, 87584, 87652, 87720, 87788, 87856, 87924, 87992, 88060, 88128, 88196, 88264, 88332, 88400, 88468, 88536, 88604, 88672, 88740, 88808, 88876, 88944, 89012, 89080, 89148, 89216, 89284, 89352, 89420, 89488, 89556, 89624, 89692, 89760, 89828, 89896, 89964, 90032, 90100, 90168, 90236, 90304, 90372, 90440, 90508, 90576, 90644, 90712, 90780, 90848, 90916, 90984, 91052, 91120, 91188, 91256, 91324, 91392, 91460, 91528, 91596, 91664, 91732, 91800, 91868, 91936, 92004, 92072, 92140, 92208, 92276, 92344, 92412, 92480, 92548, 92616, 92684, 92752, 92820, 92888, 92956, 93024, 93092, 93160, 93228, 93296, 93364, 93432, 93500, 93568, 93636, 93704, 93772, 93840, 93908, 93976, 94044, 94112, 94180, 94248, 94316, 94384, 94452, 94520, 94588, 94656, 94724, 94792, 94860, 94928, 94996, 95064, 95132, 95200, 95268, 95336, 95404, 95472, 95540, 95608, 95676, 95744, 95812, 95880, 95948, 96016, 96084, 96152, 96220, 96288, 96356, 96424, 96492, 96560, 96628, 96696, 96764, 96832, 96900, 96968, 97036, 97104, 97172, 97240, 97308, 97376, 97444, 97512, 97580, 97648, 97716, 97784, 97852, 97920, 97988, 98056, 98124, 98192, 98260, 98328, 98396, 98464, 98532, 98600, 98668, 98736, 98804, 98872, 98940, 99008, 99076, 99144, 99212, 99280, 99348, 99416, 99484, 99552, 99620, 99688, 99756, 99824, 99892, 99960
- There is a total of 1470 numbers (up to 100000) that are divisible by 68.
- The sum of these numbers is 73520580.
- The arithmetic mean of these numbers is 50014.
How to find the numbers divisible by 68?
Finding all the numbers that can be divided by 68 is essentially the same as searching for the multiples of 68: if a number N is a multiple of 68, then 68 is a divisor of N.
Indeed, if we assume that N is a multiple of 68, this means there exists an integer k such that:
Conversely, the result of N divided by 68 is this same integer k (without any remainder):
From this we can see that, theoretically, there's an infinite quantity of multiples of 68 (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 68 less than 100000):
- 1 × 68 = 68
- 2 × 68 = 136
- 3 × 68 = 204
- ...
- 1469 × 68 = 99892
- 1470 × 68 = 99960