What are the numbers divisible by 109?
109, 218, 327, 436, 545, 654, 763, 872, 981, 1090, 1199, 1308, 1417, 1526, 1635, 1744, 1853, 1962, 2071, 2180, 2289, 2398, 2507, 2616, 2725, 2834, 2943, 3052, 3161, 3270, 3379, 3488, 3597, 3706, 3815, 3924, 4033, 4142, 4251, 4360, 4469, 4578, 4687, 4796, 4905, 5014, 5123, 5232, 5341, 5450, 5559, 5668, 5777, 5886, 5995, 6104, 6213, 6322, 6431, 6540, 6649, 6758, 6867, 6976, 7085, 7194, 7303, 7412, 7521, 7630, 7739, 7848, 7957, 8066, 8175, 8284, 8393, 8502, 8611, 8720, 8829, 8938, 9047, 9156, 9265, 9374, 9483, 9592, 9701, 9810, 9919, 10028, 10137, 10246, 10355, 10464, 10573, 10682, 10791, 10900, 11009, 11118, 11227, 11336, 11445, 11554, 11663, 11772, 11881, 11990, 12099, 12208, 12317, 12426, 12535, 12644, 12753, 12862, 12971, 13080, 13189, 13298, 13407, 13516, 13625, 13734, 13843, 13952, 14061, 14170, 14279, 14388, 14497, 14606, 14715, 14824, 14933, 15042, 15151, 15260, 15369, 15478, 15587, 15696, 15805, 15914, 16023, 16132, 16241, 16350, 16459, 16568, 16677, 16786, 16895, 17004, 17113, 17222, 17331, 17440, 17549, 17658, 17767, 17876, 17985, 18094, 18203, 18312, 18421, 18530, 18639, 18748, 18857, 18966, 19075, 19184, 19293, 19402, 19511, 19620, 19729, 19838, 19947, 20056, 20165, 20274, 20383, 20492, 20601, 20710, 20819, 20928, 21037, 21146, 21255, 21364, 21473, 21582, 21691, 21800, 21909, 22018, 22127, 22236, 22345, 22454, 22563, 22672, 22781, 22890, 22999, 23108, 23217, 23326, 23435, 23544, 23653, 23762, 23871, 23980, 24089, 24198, 24307, 24416, 24525, 24634, 24743, 24852, 24961, 25070, 25179, 25288, 25397, 25506, 25615, 25724, 25833, 25942, 26051, 26160, 26269, 26378, 26487, 26596, 26705, 26814, 26923, 27032, 27141, 27250, 27359, 27468, 27577, 27686, 27795, 27904, 28013, 28122, 28231, 28340, 28449, 28558, 28667, 28776, 28885, 28994, 29103, 29212, 29321, 29430, 29539, 29648, 29757, 29866, 29975, 30084, 30193, 30302, 30411, 30520, 30629, 30738, 30847, 30956, 31065, 31174, 31283, 31392, 31501, 31610, 31719, 31828, 31937, 32046, 32155, 32264, 32373, 32482, 32591, 32700, 32809, 32918, 33027, 33136, 33245, 33354, 33463, 33572, 33681, 33790, 33899, 34008, 34117, 34226, 34335, 34444, 34553, 34662, 34771, 34880, 34989, 35098, 35207, 35316, 35425, 35534, 35643, 35752, 35861, 35970, 36079, 36188, 36297, 36406, 36515, 36624, 36733, 36842, 36951, 37060, 37169, 37278, 37387, 37496, 37605, 37714, 37823, 37932, 38041, 38150, 38259, 38368, 38477, 38586, 38695, 38804, 38913, 39022, 39131, 39240, 39349, 39458, 39567, 39676, 39785, 39894, 40003, 40112, 40221, 40330, 40439, 40548, 40657, 40766, 40875, 40984, 41093, 41202, 41311, 41420, 41529, 41638, 41747, 41856, 41965, 42074, 42183, 42292, 42401, 42510, 42619, 42728, 42837, 42946, 43055, 43164, 43273, 43382, 43491, 43600, 43709, 43818, 43927, 44036, 44145, 44254, 44363, 44472, 44581, 44690, 44799, 44908, 45017, 45126, 45235, 45344, 45453, 45562, 45671, 45780, 45889, 45998, 46107, 46216, 46325, 46434, 46543, 46652, 46761, 46870, 46979, 47088, 47197, 47306, 47415, 47524, 47633, 47742, 47851, 47960, 48069, 48178, 48287, 48396, 48505, 48614, 48723, 48832, 48941, 49050, 49159, 49268, 49377, 49486, 49595, 49704, 49813, 49922, 50031, 50140, 50249, 50358, 50467, 50576, 50685, 50794, 50903, 51012, 51121, 51230, 51339, 51448, 51557, 51666, 51775, 51884, 51993, 52102, 52211, 52320, 52429, 52538, 52647, 52756, 52865, 52974, 53083, 53192, 53301, 53410, 53519, 53628, 53737, 53846, 53955, 54064, 54173, 54282, 54391, 54500, 54609, 54718, 54827, 54936, 55045, 55154, 55263, 55372, 55481, 55590, 55699, 55808, 55917, 56026, 56135, 56244, 56353, 56462, 56571, 56680, 56789, 56898, 57007, 57116, 57225, 57334, 57443, 57552, 57661, 57770, 57879, 57988, 58097, 58206, 58315, 58424, 58533, 58642, 58751, 58860, 58969, 59078, 59187, 59296, 59405, 59514, 59623, 59732, 59841, 59950, 60059, 60168, 60277, 60386, 60495, 60604, 60713, 60822, 60931, 61040, 61149, 61258, 61367, 61476, 61585, 61694, 61803, 61912, 62021, 62130, 62239, 62348, 62457, 62566, 62675, 62784, 62893, 63002, 63111, 63220, 63329, 63438, 63547, 63656, 63765, 63874, 63983, 64092, 64201, 64310, 64419, 64528, 64637, 64746, 64855, 64964, 65073, 65182, 65291, 65400, 65509, 65618, 65727, 65836, 65945, 66054, 66163, 66272, 66381, 66490, 66599, 66708, 66817, 66926, 67035, 67144, 67253, 67362, 67471, 67580, 67689, 67798, 67907, 68016, 68125, 68234, 68343, 68452, 68561, 68670, 68779, 68888, 68997, 69106, 69215, 69324, 69433, 69542, 69651, 69760, 69869, 69978, 70087, 70196, 70305, 70414, 70523, 70632, 70741, 70850, 70959, 71068, 71177, 71286, 71395, 71504, 71613, 71722, 71831, 71940, 72049, 72158, 72267, 72376, 72485, 72594, 72703, 72812, 72921, 73030, 73139, 73248, 73357, 73466, 73575, 73684, 73793, 73902, 74011, 74120, 74229, 74338, 74447, 74556, 74665, 74774, 74883, 74992, 75101, 75210, 75319, 75428, 75537, 75646, 75755, 75864, 75973, 76082, 76191, 76300, 76409, 76518, 76627, 76736, 76845, 76954, 77063, 77172, 77281, 77390, 77499, 77608, 77717, 77826, 77935, 78044, 78153, 78262, 78371, 78480, 78589, 78698, 78807, 78916, 79025, 79134, 79243, 79352, 79461, 79570, 79679, 79788, 79897, 80006, 80115, 80224, 80333, 80442, 80551, 80660, 80769, 80878, 80987, 81096, 81205, 81314, 81423, 81532, 81641, 81750, 81859, 81968, 82077, 82186, 82295, 82404, 82513, 82622, 82731, 82840, 82949, 83058, 83167, 83276, 83385, 83494, 83603, 83712, 83821, 83930, 84039, 84148, 84257, 84366, 84475, 84584, 84693, 84802, 84911, 85020, 85129, 85238, 85347, 85456, 85565, 85674, 85783, 85892, 86001, 86110, 86219, 86328, 86437, 86546, 86655, 86764, 86873, 86982, 87091, 87200, 87309, 87418, 87527, 87636, 87745, 87854, 87963, 88072, 88181, 88290, 88399, 88508, 88617, 88726, 88835, 88944, 89053, 89162, 89271, 89380, 89489, 89598, 89707, 89816, 89925, 90034, 90143, 90252, 90361, 90470, 90579, 90688, 90797, 90906, 91015, 91124, 91233, 91342, 91451, 91560, 91669, 91778, 91887, 91996, 92105, 92214, 92323, 92432, 92541, 92650, 92759, 92868, 92977, 93086, 93195, 93304, 93413, 93522, 93631, 93740, 93849, 93958, 94067, 94176, 94285, 94394, 94503, 94612, 94721, 94830, 94939, 95048, 95157, 95266, 95375, 95484, 95593, 95702, 95811, 95920, 96029, 96138, 96247, 96356, 96465, 96574, 96683, 96792, 96901, 97010, 97119, 97228, 97337, 97446, 97555, 97664, 97773, 97882, 97991, 98100, 98209, 98318, 98427, 98536, 98645, 98754, 98863, 98972, 99081, 99190, 99299, 99408, 99517, 99626, 99735, 99844, 99953
- There is a total of 917 numbers (up to 100000) that are divisible by 109.
- The sum of these numbers is 45878427.
- The arithmetic mean of these numbers is 50031.
How to find the numbers divisible by 109?
Finding all the numbers that can be divided by 109 is essentially the same as searching for the multiples of 109: if a number N is a multiple of 109, then 109 is a divisor of N.
Indeed, if we assume that N is a multiple of 109, this means there exists an integer k such that:
Conversely, the result of N divided by 109 is this same integer k (without any remainder):
From this we can see that, theoretically, there's an infinite quantity of multiples of 109 (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 109 less than 100000):
- 1 × 109 = 109
- 2 × 109 = 218
- 3 × 109 = 327
- ...
- 916 × 109 = 99844
- 917 × 109 = 99953