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
- There is a total of 793 numbers (up to 100000) that are divisible by 126.
- The sum of these numbers is 39667446.
- The arithmetic mean of these numbers is 50022.
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:
Conversely, the result of N divided by 126 is this same integer k (without any remainder):
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