What are the numbers divisible by 99?

99, 198, 297, 396, 495, 594, 693, 792, 891, 990, 1089, 1188, 1287, 1386, 1485, 1584, 1683, 1782, 1881, 1980, 2079, 2178, 2277, 2376, 2475, 2574, 2673, 2772, 2871, 2970, 3069, 3168, 3267, 3366, 3465, 3564, 3663, 3762, 3861, 3960, 4059, 4158, 4257, 4356, 4455, 4554, 4653, 4752, 4851, 4950, 5049, 5148, 5247, 5346, 5445, 5544, 5643, 5742, 5841, 5940, 6039, 6138, 6237, 6336, 6435, 6534, 6633, 6732, 6831, 6930, 7029, 7128, 7227, 7326, 7425, 7524, 7623, 7722, 7821, 7920, 8019, 8118, 8217, 8316, 8415, 8514, 8613, 8712, 8811, 8910, 9009, 9108, 9207, 9306, 9405, 9504, 9603, 9702, 9801, 9900, 9999, 10098, 10197, 10296, 10395, 10494, 10593, 10692, 10791, 10890, 10989, 11088, 11187, 11286, 11385, 11484, 11583, 11682, 11781, 11880, 11979, 12078, 12177, 12276, 12375, 12474, 12573, 12672, 12771, 12870, 12969, 13068, 13167, 13266, 13365, 13464, 13563, 13662, 13761, 13860, 13959, 14058, 14157, 14256, 14355, 14454, 14553, 14652, 14751, 14850, 14949, 15048, 15147, 15246, 15345, 15444, 15543, 15642, 15741, 15840, 15939, 16038, 16137, 16236, 16335, 16434, 16533, 16632, 16731, 16830, 16929, 17028, 17127, 17226, 17325, 17424, 17523, 17622, 17721, 17820, 17919, 18018, 18117, 18216, 18315, 18414, 18513, 18612, 18711, 18810, 18909, 19008, 19107, 19206, 19305, 19404, 19503, 19602, 19701, 19800, 19899, 19998, 20097, 20196, 20295, 20394, 20493, 20592, 20691, 20790, 20889, 20988, 21087, 21186, 21285, 21384, 21483, 21582, 21681, 21780, 21879, 21978, 22077, 22176, 22275, 22374, 22473, 22572, 22671, 22770, 22869, 22968, 23067, 23166, 23265, 23364, 23463, 23562, 23661, 23760, 23859, 23958, 24057, 24156, 24255, 24354, 24453, 24552, 24651, 24750, 24849, 24948, 25047, 25146, 25245, 25344, 25443, 25542, 25641, 25740, 25839, 25938, 26037, 26136, 26235, 26334, 26433, 26532, 26631, 26730, 26829, 26928, 27027, 27126, 27225, 27324, 27423, 27522, 27621, 27720, 27819, 27918, 28017, 28116, 28215, 28314, 28413, 28512, 28611, 28710, 28809, 28908, 29007, 29106, 29205, 29304, 29403, 29502, 29601, 29700, 29799, 29898, 29997, 30096, 30195, 30294, 30393, 30492, 30591, 30690, 30789, 30888, 30987, 31086, 31185, 31284, 31383, 31482, 31581, 31680, 31779, 31878, 31977, 32076, 32175, 32274, 32373, 32472, 32571, 32670, 32769, 32868, 32967, 33066, 33165, 33264, 33363, 33462, 33561, 33660, 33759, 33858, 33957, 34056, 34155, 34254, 34353, 34452, 34551, 34650, 34749, 34848, 34947, 35046, 35145, 35244, 35343, 35442, 35541, 35640, 35739, 35838, 35937, 36036, 36135, 36234, 36333, 36432, 36531, 36630, 36729, 36828, 36927, 37026, 37125, 37224, 37323, 37422, 37521, 37620, 37719, 37818, 37917, 38016, 38115, 38214, 38313, 38412, 38511, 38610, 38709, 38808, 38907, 39006, 39105, 39204, 39303, 39402, 39501, 39600, 39699, 39798, 39897, 39996, 40095, 40194, 40293, 40392, 40491, 40590, 40689, 40788, 40887, 40986, 41085, 41184, 41283, 41382, 41481, 41580, 41679, 41778, 41877, 41976, 42075, 42174, 42273, 42372, 42471, 42570, 42669, 42768, 42867, 42966, 43065, 43164, 43263, 43362, 43461, 43560, 43659, 43758, 43857, 43956, 44055, 44154, 44253, 44352, 44451, 44550, 44649, 44748, 44847, 44946, 45045, 45144, 45243, 45342, 45441, 45540, 45639, 45738, 45837, 45936, 46035, 46134, 46233, 46332, 46431, 46530, 46629, 46728, 46827, 46926, 47025, 47124, 47223, 47322, 47421, 47520, 47619, 47718, 47817, 47916, 48015, 48114, 48213, 48312, 48411, 48510, 48609, 48708, 48807, 48906, 49005, 49104, 49203, 49302, 49401, 49500, 49599, 49698, 49797, 49896, 49995, 50094, 50193, 50292, 50391, 50490, 50589, 50688, 50787, 50886, 50985, 51084, 51183, 51282, 51381, 51480, 51579, 51678, 51777, 51876, 51975, 52074, 52173, 52272, 52371, 52470, 52569, 52668, 52767, 52866, 52965, 53064, 53163, 53262, 53361, 53460, 53559, 53658, 53757, 53856, 53955, 54054, 54153, 54252, 54351, 54450, 54549, 54648, 54747, 54846, 54945, 55044, 55143, 55242, 55341, 55440, 55539, 55638, 55737, 55836, 55935, 56034, 56133, 56232, 56331, 56430, 56529, 56628, 56727, 56826, 56925, 57024, 57123, 57222, 57321, 57420, 57519, 57618, 57717, 57816, 57915, 58014, 58113, 58212, 58311, 58410, 58509, 58608, 58707, 58806, 58905, 59004, 59103, 59202, 59301, 59400, 59499, 59598, 59697, 59796, 59895, 59994, 60093, 60192, 60291, 60390, 60489, 60588, 60687, 60786, 60885, 60984, 61083, 61182, 61281, 61380, 61479, 61578, 61677, 61776, 61875, 61974, 62073, 62172, 62271, 62370, 62469, 62568, 62667, 62766, 62865, 62964, 63063, 63162, 63261, 63360, 63459, 63558, 63657, 63756, 63855, 63954, 64053, 64152, 64251, 64350, 64449, 64548, 64647, 64746, 64845, 64944, 65043, 65142, 65241, 65340, 65439, 65538, 65637, 65736, 65835, 65934, 66033, 66132, 66231, 66330, 66429, 66528, 66627, 66726, 66825, 66924, 67023, 67122, 67221, 67320, 67419, 67518, 67617, 67716, 67815, 67914, 68013, 68112, 68211, 68310, 68409, 68508, 68607, 68706, 68805, 68904, 69003, 69102, 69201, 69300, 69399, 69498, 69597, 69696, 69795, 69894, 69993, 70092, 70191, 70290, 70389, 70488, 70587, 70686, 70785, 70884, 70983, 71082, 71181, 71280, 71379, 71478, 71577, 71676, 71775, 71874, 71973, 72072, 72171, 72270, 72369, 72468, 72567, 72666, 72765, 72864, 72963, 73062, 73161, 73260, 73359, 73458, 73557, 73656, 73755, 73854, 73953, 74052, 74151, 74250, 74349, 74448, 74547, 74646, 74745, 74844, 74943, 75042, 75141, 75240, 75339, 75438, 75537, 75636, 75735, 75834, 75933, 76032, 76131, 76230, 76329, 76428, 76527, 76626, 76725, 76824, 76923, 77022, 77121, 77220, 77319, 77418, 77517, 77616, 77715, 77814, 77913, 78012, 78111, 78210, 78309, 78408, 78507, 78606, 78705, 78804, 78903, 79002, 79101, 79200, 79299, 79398, 79497, 79596, 79695, 79794, 79893, 79992, 80091, 80190, 80289, 80388, 80487, 80586, 80685, 80784, 80883, 80982, 81081, 81180, 81279, 81378, 81477, 81576, 81675, 81774, 81873, 81972, 82071, 82170, 82269, 82368, 82467, 82566, 82665, 82764, 82863, 82962, 83061, 83160, 83259, 83358, 83457, 83556, 83655, 83754, 83853, 83952, 84051, 84150, 84249, 84348, 84447, 84546, 84645, 84744, 84843, 84942, 85041, 85140, 85239, 85338, 85437, 85536, 85635, 85734, 85833, 85932, 86031, 86130, 86229, 86328, 86427, 86526, 86625, 86724, 86823, 86922, 87021, 87120, 87219, 87318, 87417, 87516, 87615, 87714, 87813, 87912, 88011, 88110, 88209, 88308, 88407, 88506, 88605, 88704, 88803, 88902, 89001, 89100, 89199, 89298, 89397, 89496, 89595, 89694, 89793, 89892, 89991, 90090, 90189, 90288, 90387, 90486, 90585, 90684, 90783, 90882, 90981, 91080, 91179, 91278, 91377, 91476, 91575, 91674, 91773, 91872, 91971, 92070, 92169, 92268, 92367, 92466, 92565, 92664, 92763, 92862, 92961, 93060, 93159, 93258, 93357, 93456, 93555, 93654, 93753, 93852, 93951, 94050, 94149, 94248, 94347, 94446, 94545, 94644, 94743, 94842, 94941, 95040, 95139, 95238, 95337, 95436, 95535, 95634, 95733, 95832, 95931, 96030, 96129, 96228, 96327, 96426, 96525, 96624, 96723, 96822, 96921, 97020, 97119, 97218, 97317, 97416, 97515, 97614, 97713, 97812, 97911, 98010, 98109, 98208, 98307, 98406, 98505, 98604, 98703, 98802, 98901, 99000, 99099, 99198, 99297, 99396, 99495, 99594, 99693, 99792, 99891, 99990

How to find the numbers divisible by 99?

Finding all the numbers that can be divided by 99 is essentially the same as searching for the multiples of 99: if a number N is a multiple of 99, then 99 is a divisor of N.

Indeed, if we assume that N is a multiple of 99, this means there exists an integer k such that:

k × 99 = N

Conversely, the result of N divided by 99 is this same integer k (without any remainder):

k = N 99

From this we can see that, theoretically, there's an infinite quantity of multiples of 99 (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 99 less than 100000):

  • 1 × 99 = 99
  • 2 × 99 = 198
  • 3 × 99 = 297
  • ...
  • 1009 × 99 = 99891
  • 1010 × 99 = 99990