What are the numbers divisible by 117?

117, 234, 351, 468, 585, 702, 819, 936, 1053, 1170, 1287, 1404, 1521, 1638, 1755, 1872, 1989, 2106, 2223, 2340, 2457, 2574, 2691, 2808, 2925, 3042, 3159, 3276, 3393, 3510, 3627, 3744, 3861, 3978, 4095, 4212, 4329, 4446, 4563, 4680, 4797, 4914, 5031, 5148, 5265, 5382, 5499, 5616, 5733, 5850, 5967, 6084, 6201, 6318, 6435, 6552, 6669, 6786, 6903, 7020, 7137, 7254, 7371, 7488, 7605, 7722, 7839, 7956, 8073, 8190, 8307, 8424, 8541, 8658, 8775, 8892, 9009, 9126, 9243, 9360, 9477, 9594, 9711, 9828, 9945, 10062, 10179, 10296, 10413, 10530, 10647, 10764, 10881, 10998, 11115, 11232, 11349, 11466, 11583, 11700, 11817, 11934, 12051, 12168, 12285, 12402, 12519, 12636, 12753, 12870, 12987, 13104, 13221, 13338, 13455, 13572, 13689, 13806, 13923, 14040, 14157, 14274, 14391, 14508, 14625, 14742, 14859, 14976, 15093, 15210, 15327, 15444, 15561, 15678, 15795, 15912, 16029, 16146, 16263, 16380, 16497, 16614, 16731, 16848, 16965, 17082, 17199, 17316, 17433, 17550, 17667, 17784, 17901, 18018, 18135, 18252, 18369, 18486, 18603, 18720, 18837, 18954, 19071, 19188, 19305, 19422, 19539, 19656, 19773, 19890, 20007, 20124, 20241, 20358, 20475, 20592, 20709, 20826, 20943, 21060, 21177, 21294, 21411, 21528, 21645, 21762, 21879, 21996, 22113, 22230, 22347, 22464, 22581, 22698, 22815, 22932, 23049, 23166, 23283, 23400, 23517, 23634, 23751, 23868, 23985, 24102, 24219, 24336, 24453, 24570, 24687, 24804, 24921, 25038, 25155, 25272, 25389, 25506, 25623, 25740, 25857, 25974, 26091, 26208, 26325, 26442, 26559, 26676, 26793, 26910, 27027, 27144, 27261, 27378, 27495, 27612, 27729, 27846, 27963, 28080, 28197, 28314, 28431, 28548, 28665, 28782, 28899, 29016, 29133, 29250, 29367, 29484, 29601, 29718, 29835, 29952, 30069, 30186, 30303, 30420, 30537, 30654, 30771, 30888, 31005, 31122, 31239, 31356, 31473, 31590, 31707, 31824, 31941, 32058, 32175, 32292, 32409, 32526, 32643, 32760, 32877, 32994, 33111, 33228, 33345, 33462, 33579, 33696, 33813, 33930, 34047, 34164, 34281, 34398, 34515, 34632, 34749, 34866, 34983, 35100, 35217, 35334, 35451, 35568, 35685, 35802, 35919, 36036, 36153, 36270, 36387, 36504, 36621, 36738, 36855, 36972, 37089, 37206, 37323, 37440, 37557, 37674, 37791, 37908, 38025, 38142, 38259, 38376, 38493, 38610, 38727, 38844, 38961, 39078, 39195, 39312, 39429, 39546, 39663, 39780, 39897, 40014, 40131, 40248, 40365, 40482, 40599, 40716, 40833, 40950, 41067, 41184, 41301, 41418, 41535, 41652, 41769, 41886, 42003, 42120, 42237, 42354, 42471, 42588, 42705, 42822, 42939, 43056, 43173, 43290, 43407, 43524, 43641, 43758, 43875, 43992, 44109, 44226, 44343, 44460, 44577, 44694, 44811, 44928, 45045, 45162, 45279, 45396, 45513, 45630, 45747, 45864, 45981, 46098, 46215, 46332, 46449, 46566, 46683, 46800, 46917, 47034, 47151, 47268, 47385, 47502, 47619, 47736, 47853, 47970, 48087, 48204, 48321, 48438, 48555, 48672, 48789, 48906, 49023, 49140, 49257, 49374, 49491, 49608, 49725, 49842, 49959, 50076, 50193, 50310, 50427, 50544, 50661, 50778, 50895, 51012, 51129, 51246, 51363, 51480, 51597, 51714, 51831, 51948, 52065, 52182, 52299, 52416, 52533, 52650, 52767, 52884, 53001, 53118, 53235, 53352, 53469, 53586, 53703, 53820, 53937, 54054, 54171, 54288, 54405, 54522, 54639, 54756, 54873, 54990, 55107, 55224, 55341, 55458, 55575, 55692, 55809, 55926, 56043, 56160, 56277, 56394, 56511, 56628, 56745, 56862, 56979, 57096, 57213, 57330, 57447, 57564, 57681, 57798, 57915, 58032, 58149, 58266, 58383, 58500, 58617, 58734, 58851, 58968, 59085, 59202, 59319, 59436, 59553, 59670, 59787, 59904, 60021, 60138, 60255, 60372, 60489, 60606, 60723, 60840, 60957, 61074, 61191, 61308, 61425, 61542, 61659, 61776, 61893, 62010, 62127, 62244, 62361, 62478, 62595, 62712, 62829, 62946, 63063, 63180, 63297, 63414, 63531, 63648, 63765, 63882, 63999, 64116, 64233, 64350, 64467, 64584, 64701, 64818, 64935, 65052, 65169, 65286, 65403, 65520, 65637, 65754, 65871, 65988, 66105, 66222, 66339, 66456, 66573, 66690, 66807, 66924, 67041, 67158, 67275, 67392, 67509, 67626, 67743, 67860, 67977, 68094, 68211, 68328, 68445, 68562, 68679, 68796, 68913, 69030, 69147, 69264, 69381, 69498, 69615, 69732, 69849, 69966, 70083, 70200, 70317, 70434, 70551, 70668, 70785, 70902, 71019, 71136, 71253, 71370, 71487, 71604, 71721, 71838, 71955, 72072, 72189, 72306, 72423, 72540, 72657, 72774, 72891, 73008, 73125, 73242, 73359, 73476, 73593, 73710, 73827, 73944, 74061, 74178, 74295, 74412, 74529, 74646, 74763, 74880, 74997, 75114, 75231, 75348, 75465, 75582, 75699, 75816, 75933, 76050, 76167, 76284, 76401, 76518, 76635, 76752, 76869, 76986, 77103, 77220, 77337, 77454, 77571, 77688, 77805, 77922, 78039, 78156, 78273, 78390, 78507, 78624, 78741, 78858, 78975, 79092, 79209, 79326, 79443, 79560, 79677, 79794, 79911, 80028, 80145, 80262, 80379, 80496, 80613, 80730, 80847, 80964, 81081, 81198, 81315, 81432, 81549, 81666, 81783, 81900, 82017, 82134, 82251, 82368, 82485, 82602, 82719, 82836, 82953, 83070, 83187, 83304, 83421, 83538, 83655, 83772, 83889, 84006, 84123, 84240, 84357, 84474, 84591, 84708, 84825, 84942, 85059, 85176, 85293, 85410, 85527, 85644, 85761, 85878, 85995, 86112, 86229, 86346, 86463, 86580, 86697, 86814, 86931, 87048, 87165, 87282, 87399, 87516, 87633, 87750, 87867, 87984, 88101, 88218, 88335, 88452, 88569, 88686, 88803, 88920, 89037, 89154, 89271, 89388, 89505, 89622, 89739, 89856, 89973, 90090, 90207, 90324, 90441, 90558, 90675, 90792, 90909, 91026, 91143, 91260, 91377, 91494, 91611, 91728, 91845, 91962, 92079, 92196, 92313, 92430, 92547, 92664, 92781, 92898, 93015, 93132, 93249, 93366, 93483, 93600, 93717, 93834, 93951, 94068, 94185, 94302, 94419, 94536, 94653, 94770, 94887, 95004, 95121, 95238, 95355, 95472, 95589, 95706, 95823, 95940, 96057, 96174, 96291, 96408, 96525, 96642, 96759, 96876, 96993, 97110, 97227, 97344, 97461, 97578, 97695, 97812, 97929, 98046, 98163, 98280, 98397, 98514, 98631, 98748, 98865, 98982, 99099, 99216, 99333, 99450, 99567, 99684, 99801, 99918

How to find the numbers divisible by 117?

Finding all the numbers that can be divided by 117 is essentially the same as searching for the multiples of 117: if a number N is a multiple of 117, then 117 is a divisor of N.

Indeed, if we assume that N is a multiple of 117, this means there exists an integer k such that:

k × 117 = N

Conversely, the result of N divided by 117 is this same integer k (without any remainder):

k = N 117

From this we can see that, theoretically, there's an infinite quantity of multiples of 117 (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 117 less than 100000):

  • 1 × 117 = 117
  • 2 × 117 = 234
  • 3 × 117 = 351
  • ...
  • 853 × 117 = 99801
  • 854 × 117 = 99918