What are the numbers divisible by 126?

126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260, 1386, 1512, 1638, 1764, 1890, 2016, 2142, 2268, 2394, 2520, 2646, 2772, 2898, 3024, 3150, 3276, 3402, 3528, 3654, 3780, 3906, 4032, 4158, 4284, 4410, 4536, 4662, 4788, 4914, 5040, 5166, 5292, 5418, 5544, 5670, 5796, 5922, 6048, 6174, 6300, 6426, 6552, 6678, 6804, 6930, 7056, 7182, 7308, 7434, 7560, 7686, 7812, 7938, 8064, 8190, 8316, 8442, 8568, 8694, 8820, 8946, 9072, 9198, 9324, 9450, 9576, 9702, 9828, 9954, 10080, 10206, 10332, 10458, 10584, 10710, 10836, 10962, 11088, 11214, 11340, 11466, 11592, 11718, 11844, 11970, 12096, 12222, 12348, 12474, 12600, 12726, 12852, 12978, 13104, 13230, 13356, 13482, 13608, 13734, 13860, 13986, 14112, 14238, 14364, 14490, 14616, 14742, 14868, 14994, 15120, 15246, 15372, 15498, 15624, 15750, 15876, 16002, 16128, 16254, 16380, 16506, 16632, 16758, 16884, 17010, 17136, 17262, 17388, 17514, 17640, 17766, 17892, 18018, 18144, 18270, 18396, 18522, 18648, 18774, 18900, 19026, 19152, 19278, 19404, 19530, 19656, 19782, 19908, 20034, 20160, 20286, 20412, 20538, 20664, 20790, 20916, 21042, 21168, 21294, 21420, 21546, 21672, 21798, 21924, 22050, 22176, 22302, 22428, 22554, 22680, 22806, 22932, 23058, 23184, 23310, 23436, 23562, 23688, 23814, 23940, 24066, 24192, 24318, 24444, 24570, 24696, 24822, 24948, 25074, 25200, 25326, 25452, 25578, 25704, 25830, 25956, 26082, 26208, 26334, 26460, 26586, 26712, 26838, 26964, 27090, 27216, 27342, 27468, 27594, 27720, 27846, 27972, 28098, 28224, 28350, 28476, 28602, 28728, 28854, 28980, 29106, 29232, 29358, 29484, 29610, 29736, 29862, 29988, 30114, 30240, 30366, 30492, 30618, 30744, 30870, 30996, 31122, 31248, 31374, 31500, 31626, 31752, 31878, 32004, 32130, 32256, 32382, 32508, 32634, 32760, 32886, 33012, 33138, 33264, 33390, 33516, 33642, 33768, 33894, 34020, 34146, 34272, 34398, 34524, 34650, 34776, 34902, 35028, 35154, 35280, 35406, 35532, 35658, 35784, 35910, 36036, 36162, 36288, 36414, 36540, 36666, 36792, 36918, 37044, 37170, 37296, 37422, 37548, 37674, 37800, 37926, 38052, 38178, 38304, 38430, 38556, 38682, 38808, 38934, 39060, 39186, 39312, 39438, 39564, 39690, 39816, 39942, 40068, 40194, 40320, 40446, 40572, 40698, 40824, 40950, 41076, 41202, 41328, 41454, 41580, 41706, 41832, 41958, 42084, 42210, 42336, 42462, 42588, 42714, 42840, 42966, 43092, 43218, 43344, 43470, 43596, 43722, 43848, 43974, 44100, 44226, 44352, 44478, 44604, 44730, 44856, 44982, 45108, 45234, 45360, 45486, 45612, 45738, 45864, 45990, 46116, 46242, 46368, 46494, 46620, 46746, 46872, 46998, 47124, 47250, 47376, 47502, 47628, 47754, 47880, 48006, 48132, 48258, 48384, 48510, 48636, 48762, 48888, 49014, 49140, 49266, 49392, 49518, 49644, 49770, 49896, 50022, 50148, 50274, 50400, 50526, 50652, 50778, 50904, 51030, 51156, 51282, 51408, 51534, 51660, 51786, 51912, 52038, 52164, 52290, 52416, 52542, 52668, 52794, 52920, 53046, 53172, 53298, 53424, 53550, 53676, 53802, 53928, 54054, 54180, 54306, 54432, 54558, 54684, 54810, 54936, 55062, 55188, 55314, 55440, 55566, 55692, 55818, 55944, 56070, 56196, 56322, 56448, 56574, 56700, 56826, 56952, 57078, 57204, 57330, 57456, 57582, 57708, 57834, 57960, 58086, 58212, 58338, 58464, 58590, 58716, 58842, 58968, 59094, 59220, 59346, 59472, 59598, 59724, 59850, 59976, 60102, 60228, 60354, 60480, 60606, 60732, 60858, 60984, 61110, 61236, 61362, 61488, 61614, 61740, 61866, 61992, 62118, 62244, 62370, 62496, 62622, 62748, 62874, 63000, 63126, 63252, 63378, 63504, 63630, 63756, 63882, 64008, 64134, 64260, 64386, 64512, 64638, 64764, 64890, 65016, 65142, 65268, 65394, 65520, 65646, 65772, 65898, 66024, 66150, 66276, 66402, 66528, 66654, 66780, 66906, 67032, 67158, 67284, 67410, 67536, 67662, 67788, 67914, 68040, 68166, 68292, 68418, 68544, 68670, 68796, 68922, 69048, 69174, 69300, 69426, 69552, 69678, 69804, 69930, 70056, 70182, 70308, 70434, 70560, 70686, 70812, 70938, 71064, 71190, 71316, 71442, 71568, 71694, 71820, 71946, 72072, 72198, 72324, 72450, 72576, 72702, 72828, 72954, 73080, 73206, 73332, 73458, 73584, 73710, 73836, 73962, 74088, 74214, 74340, 74466, 74592, 74718, 74844, 74970, 75096, 75222, 75348, 75474, 75600, 75726, 75852, 75978, 76104, 76230, 76356, 76482, 76608, 76734, 76860, 76986, 77112, 77238, 77364, 77490, 77616, 77742, 77868, 77994, 78120, 78246, 78372, 78498, 78624, 78750, 78876, 79002, 79128, 79254, 79380, 79506, 79632, 79758, 79884, 80010, 80136, 80262, 80388, 80514, 80640, 80766, 80892, 81018, 81144, 81270, 81396, 81522, 81648, 81774, 81900, 82026, 82152, 82278, 82404, 82530, 82656, 82782, 82908, 83034, 83160, 83286, 83412, 83538, 83664, 83790, 83916, 84042, 84168, 84294, 84420, 84546, 84672, 84798, 84924, 85050, 85176, 85302, 85428, 85554, 85680, 85806, 85932, 86058, 86184, 86310, 86436, 86562, 86688, 86814, 86940, 87066, 87192, 87318, 87444, 87570, 87696, 87822, 87948, 88074, 88200, 88326, 88452, 88578, 88704, 88830, 88956, 89082, 89208, 89334, 89460, 89586, 89712, 89838, 89964, 90090, 90216, 90342, 90468, 90594, 90720, 90846, 90972, 91098, 91224, 91350, 91476, 91602, 91728, 91854, 91980, 92106, 92232, 92358, 92484, 92610, 92736, 92862, 92988, 93114, 93240, 93366, 93492, 93618, 93744, 93870, 93996, 94122, 94248, 94374, 94500, 94626, 94752, 94878, 95004, 95130, 95256, 95382, 95508, 95634, 95760, 95886, 96012, 96138, 96264, 96390, 96516, 96642, 96768, 96894, 97020, 97146, 97272, 97398, 97524, 97650, 97776, 97902, 98028, 98154, 98280, 98406, 98532, 98658, 98784, 98910, 99036, 99162, 99288, 99414, 99540, 99666, 99792, 99918

How to find the numbers divisible by 126?

Finding all the numbers that can be divided by 126 is essentially the same as searching for the multiples of 126: if a number N is a multiple of 126, then 126 is a divisor of N.

Indeed, if we assume that N is a multiple of 126, this means there exists an integer k such that:

k × 126 = N

Conversely, the result of N divided by 126 is this same integer k (without any remainder):

k = N 126

From this we can see that, theoretically, there's an infinite quantity of multiples of 126 (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 126 less than 100000):

  • 1 × 126 = 126
  • 2 × 126 = 252
  • 3 × 126 = 378
  • ...
  • 792 × 126 = 99792
  • 793 × 126 = 99918