What are the numbers divisible by 51?
51, 102, 153, 204, 255, 306, 357, 408, 459, 510, 561, 612, 663, 714, 765, 816, 867, 918, 969, 1020, 1071, 1122, 1173, 1224, 1275, 1326, 1377, 1428, 1479, 1530, 1581, 1632, 1683, 1734, 1785, 1836, 1887, 1938, 1989, 2040, 2091, 2142, 2193, 2244, 2295, 2346, 2397, 2448, 2499, 2550, 2601, 2652, 2703, 2754, 2805, 2856, 2907, 2958, 3009, 3060, 3111, 3162, 3213, 3264, 3315, 3366, 3417, 3468, 3519, 3570, 3621, 3672, 3723, 3774, 3825, 3876, 3927, 3978, 4029, 4080, 4131, 4182, 4233, 4284, 4335, 4386, 4437, 4488, 4539, 4590, 4641, 4692, 4743, 4794, 4845, 4896, 4947, 4998, 5049, 5100, 5151, 5202, 5253, 5304, 5355, 5406, 5457, 5508, 5559, 5610, 5661, 5712, 5763, 5814, 5865, 5916, 5967, 6018, 6069, 6120, 6171, 6222, 6273, 6324, 6375, 6426, 6477, 6528, 6579, 6630, 6681, 6732, 6783, 6834, 6885, 6936, 6987, 7038, 7089, 7140, 7191, 7242, 7293, 7344, 7395, 7446, 7497, 7548, 7599, 7650, 7701, 7752, 7803, 7854, 7905, 7956, 8007, 8058, 8109, 8160, 8211, 8262, 8313, 8364, 8415, 8466, 8517, 8568, 8619, 8670, 8721, 8772, 8823, 8874, 8925, 8976, 9027, 9078, 9129, 9180, 9231, 9282, 9333, 9384, 9435, 9486, 9537, 9588, 9639, 9690, 9741, 9792, 9843, 9894, 9945, 9996, 10047, 10098, 10149, 10200, 10251, 10302, 10353, 10404, 10455, 10506, 10557, 10608, 10659, 10710, 10761, 10812, 10863, 10914, 10965, 11016, 11067, 11118, 11169, 11220, 11271, 11322, 11373, 11424, 11475, 11526, 11577, 11628, 11679, 11730, 11781, 11832, 11883, 11934, 11985, 12036, 12087, 12138, 12189, 12240, 12291, 12342, 12393, 12444, 12495, 12546, 12597, 12648, 12699, 12750, 12801, 12852, 12903, 12954, 13005, 13056, 13107, 13158, 13209, 13260, 13311, 13362, 13413, 13464, 13515, 13566, 13617, 13668, 13719, 13770, 13821, 13872, 13923, 13974, 14025, 14076, 14127, 14178, 14229, 14280, 14331, 14382, 14433, 14484, 14535, 14586, 14637, 14688, 14739, 14790, 14841, 14892, 14943, 14994, 15045, 15096, 15147, 15198, 15249, 15300, 15351, 15402, 15453, 15504, 15555, 15606, 15657, 15708, 15759, 15810, 15861, 15912, 15963, 16014, 16065, 16116, 16167, 16218, 16269, 16320, 16371, 16422, 16473, 16524, 16575, 16626, 16677, 16728, 16779, 16830, 16881, 16932, 16983, 17034, 17085, 17136, 17187, 17238, 17289, 17340, 17391, 17442, 17493, 17544, 17595, 17646, 17697, 17748, 17799, 17850, 17901, 17952, 18003, 18054, 18105, 18156, 18207, 18258, 18309, 18360, 18411, 18462, 18513, 18564, 18615, 18666, 18717, 18768, 18819, 18870, 18921, 18972, 19023, 19074, 19125, 19176, 19227, 19278, 19329, 19380, 19431, 19482, 19533, 19584, 19635, 19686, 19737, 19788, 19839, 19890, 19941, 19992, 20043, 20094, 20145, 20196, 20247, 20298, 20349, 20400, 20451, 20502, 20553, 20604, 20655, 20706, 20757, 20808, 20859, 20910, 20961, 21012, 21063, 21114, 21165, 21216, 21267, 21318, 21369, 21420, 21471, 21522, 21573, 21624, 21675, 21726, 21777, 21828, 21879, 21930, 21981, 22032, 22083, 22134, 22185, 22236, 22287, 22338, 22389, 22440, 22491, 22542, 22593, 22644, 22695, 22746, 22797, 22848, 22899, 22950, 23001, 23052, 23103, 23154, 23205, 23256, 23307, 23358, 23409, 23460, 23511, 23562, 23613, 23664, 23715, 23766, 23817, 23868, 23919, 23970, 24021, 24072, 24123, 24174, 24225, 24276, 24327, 24378, 24429, 24480, 24531, 24582, 24633, 24684, 24735, 24786, 24837, 24888, 24939, 24990, 25041, 25092, 25143, 25194, 25245, 25296, 25347, 25398, 25449, 25500, 25551, 25602, 25653, 25704, 25755, 25806, 25857, 25908, 25959, 26010, 26061, 26112, 26163, 26214, 26265, 26316, 26367, 26418, 26469, 26520, 26571, 26622, 26673, 26724, 26775, 26826, 26877, 26928, 26979, 27030, 27081, 27132, 27183, 27234, 27285, 27336, 27387, 27438, 27489, 27540, 27591, 27642, 27693, 27744, 27795, 27846, 27897, 27948, 27999, 28050, 28101, 28152, 28203, 28254, 28305, 28356, 28407, 28458, 28509, 28560, 28611, 28662, 28713, 28764, 28815, 28866, 28917, 28968, 29019, 29070, 29121, 29172, 29223, 29274, 29325, 29376, 29427, 29478, 29529, 29580, 29631, 29682, 29733, 29784, 29835, 29886, 29937, 29988, 30039, 30090, 30141, 30192, 30243, 30294, 30345, 30396, 30447, 30498, 30549, 30600, 30651, 30702, 30753, 30804, 30855, 30906, 30957, 31008, 31059, 31110, 31161, 31212, 31263, 31314, 31365, 31416, 31467, 31518, 31569, 31620, 31671, 31722, 31773, 31824, 31875, 31926, 31977, 32028, 32079, 32130, 32181, 32232, 32283, 32334, 32385, 32436, 32487, 32538, 32589, 32640, 32691, 32742, 32793, 32844, 32895, 32946, 32997, 33048, 33099, 33150, 33201, 33252, 33303, 33354, 33405, 33456, 33507, 33558, 33609, 33660, 33711, 33762, 33813, 33864, 33915, 33966, 34017, 34068, 34119, 34170, 34221, 34272, 34323, 34374, 34425, 34476, 34527, 34578, 34629, 34680, 34731, 34782, 34833, 34884, 34935, 34986, 35037, 35088, 35139, 35190, 35241, 35292, 35343, 35394, 35445, 35496, 35547, 35598, 35649, 35700, 35751, 35802, 35853, 35904, 35955, 36006, 36057, 36108, 36159, 36210, 36261, 36312, 36363, 36414, 36465, 36516, 36567, 36618, 36669, 36720, 36771, 36822, 36873, 36924, 36975, 37026, 37077, 37128, 37179, 37230, 37281, 37332, 37383, 37434, 37485, 37536, 37587, 37638, 37689, 37740, 37791, 37842, 37893, 37944, 37995, 38046, 38097, 38148, 38199, 38250, 38301, 38352, 38403, 38454, 38505, 38556, 38607, 38658, 38709, 38760, 38811, 38862, 38913, 38964, 39015, 39066, 39117, 39168, 39219, 39270, 39321, 39372, 39423, 39474, 39525, 39576, 39627, 39678, 39729, 39780, 39831, 39882, 39933, 39984, 40035, 40086, 40137, 40188, 40239, 40290, 40341, 40392, 40443, 40494, 40545, 40596, 40647, 40698, 40749, 40800, 40851, 40902, 40953, 41004, 41055, 41106, 41157, 41208, 41259, 41310, 41361, 41412, 41463, 41514, 41565, 41616, 41667, 41718, 41769, 41820, 41871, 41922, 41973, 42024, 42075, 42126, 42177, 42228, 42279, 42330, 42381, 42432, 42483, 42534, 42585, 42636, 42687, 42738, 42789, 42840, 42891, 42942, 42993, 43044, 43095, 43146, 43197, 43248, 43299, 43350, 43401, 43452, 43503, 43554, 43605, 43656, 43707, 43758, 43809, 43860, 43911, 43962, 44013, 44064, 44115, 44166, 44217, 44268, 44319, 44370, 44421, 44472, 44523, 44574, 44625, 44676, 44727, 44778, 44829, 44880, 44931, 44982, 45033, 45084, 45135, 45186, 45237, 45288, 45339, 45390, 45441, 45492, 45543, 45594, 45645, 45696, 45747, 45798, 45849, 45900, 45951, 46002, 46053, 46104, 46155, 46206, 46257, 46308, 46359, 46410, 46461, 46512, 46563, 46614, 46665, 46716, 46767, 46818, 46869, 46920, 46971, 47022, 47073, 47124, 47175, 47226, 47277, 47328, 47379, 47430, 47481, 47532, 47583, 47634, 47685, 47736, 47787, 47838, 47889, 47940, 47991, 48042, 48093, 48144, 48195, 48246, 48297, 48348, 48399, 48450, 48501, 48552, 48603, 48654, 48705, 48756, 48807, 48858, 48909, 48960, 49011, 49062, 49113, 49164, 49215, 49266, 49317, 49368, 49419, 49470, 49521, 49572, 49623, 49674, 49725, 49776, 49827, 49878, 49929, 49980, 50031, 50082, 50133, 50184, 50235, 50286, 50337, 50388, 50439, 50490, 50541, 50592, 50643, 50694, 50745, 50796, 50847, 50898, 50949, 51000, 51051, 51102, 51153, 51204, 51255, 51306, 51357, 51408, 51459, 51510, 51561, 51612, 51663, 51714, 51765, 51816, 51867, 51918, 51969, 52020, 52071, 52122, 52173, 52224, 52275, 52326, 52377, 52428, 52479, 52530, 52581, 52632, 52683, 52734, 52785, 52836, 52887, 52938, 52989, 53040, 53091, 53142, 53193, 53244, 53295, 53346, 53397, 53448, 53499, 53550, 53601, 53652, 53703, 53754, 53805, 53856, 53907, 53958, 54009, 54060, 54111, 54162, 54213, 54264, 54315, 54366, 54417, 54468, 54519, 54570, 54621, 54672, 54723, 54774, 54825, 54876, 54927, 54978, 55029, 55080, 55131, 55182, 55233, 55284, 55335, 55386, 55437, 55488, 55539, 55590, 55641, 55692, 55743, 55794, 55845, 55896, 55947, 55998, 56049, 56100, 56151, 56202, 56253, 56304, 56355, 56406, 56457, 56508, 56559, 56610, 56661, 56712, 56763, 56814, 56865, 56916, 56967, 57018, 57069, 57120, 57171, 57222, 57273, 57324, 57375, 57426, 57477, 57528, 57579, 57630, 57681, 57732, 57783, 57834, 57885, 57936, 57987, 58038, 58089, 58140, 58191, 58242, 58293, 58344, 58395, 58446, 58497, 58548, 58599, 58650, 58701, 58752, 58803, 58854, 58905, 58956, 59007, 59058, 59109, 59160, 59211, 59262, 59313, 59364, 59415, 59466, 59517, 59568, 59619, 59670, 59721, 59772, 59823, 59874, 59925, 59976, 60027, 60078, 60129, 60180, 60231, 60282, 60333, 60384, 60435, 60486, 60537, 60588, 60639, 60690, 60741, 60792, 60843, 60894, 60945, 60996, 61047, 61098, 61149, 61200, 61251, 61302, 61353, 61404, 61455, 61506, 61557, 61608, 61659, 61710, 61761, 61812, 61863, 61914, 61965, 62016, 62067, 62118, 62169, 62220, 62271, 62322, 62373, 62424, 62475, 62526, 62577, 62628, 62679, 62730, 62781, 62832, 62883, 62934, 62985, 63036, 63087, 63138, 63189, 63240, 63291, 63342, 63393, 63444, 63495, 63546, 63597, 63648, 63699, 63750, 63801, 63852, 63903, 63954, 64005, 64056, 64107, 64158, 64209, 64260, 64311, 64362, 64413, 64464, 64515, 64566, 64617, 64668, 64719, 64770, 64821, 64872, 64923, 64974, 65025, 65076, 65127, 65178, 65229, 65280, 65331, 65382, 65433, 65484, 65535, 65586, 65637, 65688, 65739, 65790, 65841, 65892, 65943, 65994, 66045, 66096, 66147, 66198, 66249, 66300, 66351, 66402, 66453, 66504, 66555, 66606, 66657, 66708, 66759, 66810, 66861, 66912, 66963, 67014, 67065, 67116, 67167, 67218, 67269, 67320, 67371, 67422, 67473, 67524, 67575, 67626, 67677, 67728, 67779, 67830, 67881, 67932, 67983, 68034, 68085, 68136, 68187, 68238, 68289, 68340, 68391, 68442, 68493, 68544, 68595, 68646, 68697, 68748, 68799, 68850, 68901, 68952, 69003, 69054, 69105, 69156, 69207, 69258, 69309, 69360, 69411, 69462, 69513, 69564, 69615, 69666, 69717, 69768, 69819, 69870, 69921, 69972, 70023, 70074, 70125, 70176, 70227, 70278, 70329, 70380, 70431, 70482, 70533, 70584, 70635, 70686, 70737, 70788, 70839, 70890, 70941, 70992, 71043, 71094, 71145, 71196, 71247, 71298, 71349, 71400, 71451, 71502, 71553, 71604, 71655, 71706, 71757, 71808, 71859, 71910, 71961, 72012, 72063, 72114, 72165, 72216, 72267, 72318, 72369, 72420, 72471, 72522, 72573, 72624, 72675, 72726, 72777, 72828, 72879, 72930, 72981, 73032, 73083, 73134, 73185, 73236, 73287, 73338, 73389, 73440, 73491, 73542, 73593, 73644, 73695, 73746, 73797, 73848, 73899, 73950, 74001, 74052, 74103, 74154, 74205, 74256, 74307, 74358, 74409, 74460, 74511, 74562, 74613, 74664, 74715, 74766, 74817, 74868, 74919, 74970, 75021, 75072, 75123, 75174, 75225, 75276, 75327, 75378, 75429, 75480, 75531, 75582, 75633, 75684, 75735, 75786, 75837, 75888, 75939, 75990, 76041, 76092, 76143, 76194, 76245, 76296, 76347, 76398, 76449, 76500, 76551, 76602, 76653, 76704, 76755, 76806, 76857, 76908, 76959, 77010, 77061, 77112, 77163, 77214, 77265, 77316, 77367, 77418, 77469, 77520, 77571, 77622, 77673, 77724, 77775, 77826, 77877, 77928, 77979, 78030, 78081, 78132, 78183, 78234, 78285, 78336, 78387, 78438, 78489, 78540, 78591, 78642, 78693, 78744, 78795, 78846, 78897, 78948, 78999, 79050, 79101, 79152, 79203, 79254, 79305, 79356, 79407, 79458, 79509, 79560, 79611, 79662, 79713, 79764, 79815, 79866, 79917, 79968, 80019, 80070, 80121, 80172, 80223, 80274, 80325, 80376, 80427, 80478, 80529, 80580, 80631, 80682, 80733, 80784, 80835, 80886, 80937, 80988, 81039, 81090, 81141, 81192, 81243, 81294, 81345, 81396, 81447, 81498, 81549, 81600, 81651, 81702, 81753, 81804, 81855, 81906, 81957, 82008, 82059, 82110, 82161, 82212, 82263, 82314, 82365, 82416, 82467, 82518, 82569, 82620, 82671, 82722, 82773, 82824, 82875, 82926, 82977, 83028, 83079, 83130, 83181, 83232, 83283, 83334, 83385, 83436, 83487, 83538, 83589, 83640, 83691, 83742, 83793, 83844, 83895, 83946, 83997, 84048, 84099, 84150, 84201, 84252, 84303, 84354, 84405, 84456, 84507, 84558, 84609, 84660, 84711, 84762, 84813, 84864, 84915, 84966, 85017, 85068, 85119, 85170, 85221, 85272, 85323, 85374, 85425, 85476, 85527, 85578, 85629, 85680, 85731, 85782, 85833, 85884, 85935, 85986, 86037, 86088, 86139, 86190, 86241, 86292, 86343, 86394, 86445, 86496, 86547, 86598, 86649, 86700, 86751, 86802, 86853, 86904, 86955, 87006, 87057, 87108, 87159, 87210, 87261, 87312, 87363, 87414, 87465, 87516, 87567, 87618, 87669, 87720, 87771, 87822, 87873, 87924, 87975, 88026, 88077, 88128, 88179, 88230, 88281, 88332, 88383, 88434, 88485, 88536, 88587, 88638, 88689, 88740, 88791, 88842, 88893, 88944, 88995, 89046, 89097, 89148, 89199, 89250, 89301, 89352, 89403, 89454, 89505, 89556, 89607, 89658, 89709, 89760, 89811, 89862, 89913, 89964, 90015, 90066, 90117, 90168, 90219, 90270, 90321, 90372, 90423, 90474, 90525, 90576, 90627, 90678, 90729, 90780, 90831, 90882, 90933, 90984, 91035, 91086, 91137, 91188, 91239, 91290, 91341, 91392, 91443, 91494, 91545, 91596, 91647, 91698, 91749, 91800, 91851, 91902, 91953, 92004, 92055, 92106, 92157, 92208, 92259, 92310, 92361, 92412, 92463, 92514, 92565, 92616, 92667, 92718, 92769, 92820, 92871, 92922, 92973, 93024, 93075, 93126, 93177, 93228, 93279, 93330, 93381, 93432, 93483, 93534, 93585, 93636, 93687, 93738, 93789, 93840, 93891, 93942, 93993, 94044, 94095, 94146, 94197, 94248, 94299, 94350, 94401, 94452, 94503, 94554, 94605, 94656, 94707, 94758, 94809, 94860, 94911, 94962, 95013, 95064, 95115, 95166, 95217, 95268, 95319, 95370, 95421, 95472, 95523, 95574, 95625, 95676, 95727, 95778, 95829, 95880, 95931, 95982, 96033, 96084, 96135, 96186, 96237, 96288, 96339, 96390, 96441, 96492, 96543, 96594, 96645, 96696, 96747, 96798, 96849, 96900, 96951, 97002, 97053, 97104, 97155, 97206, 97257, 97308, 97359, 97410, 97461, 97512, 97563, 97614, 97665, 97716, 97767, 97818, 97869, 97920, 97971, 98022, 98073, 98124, 98175, 98226, 98277, 98328, 98379, 98430, 98481, 98532, 98583, 98634, 98685, 98736, 98787, 98838, 98889, 98940, 98991, 99042, 99093, 99144, 99195, 99246, 99297, 99348, 99399, 99450, 99501, 99552, 99603, 99654, 99705, 99756, 99807, 99858, 99909, 99960
- There is a total of 1960 numbers (up to 100000) that are divisible by 51.
- The sum of these numbers is 98010780.
- The arithmetic mean of these numbers is 50005.5.
How to find the numbers divisible by 51?
Finding all the numbers that can be divided by 51 is essentially the same as searching for the multiples of 51: if a number N is a multiple of 51, then 51 is a divisor of N.
Indeed, if we assume that N is a multiple of 51, this means there exists an integer k such that:
Conversely, the result of N divided by 51 is this same integer k (without any remainder):
From this we can see that, theoretically, there's an infinite quantity of multiples of 51 (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 51 less than 100000):
- 1 × 51 = 51
- 2 × 51 = 102
- 3 × 51 = 153
- ...
- 1959 × 51 = 99909
- 1960 × 51 = 99960