What are the numbers divisible by 231?
231, 462, 693, 924, 1155, 1386, 1617, 1848, 2079, 2310, 2541, 2772, 3003, 3234, 3465, 3696, 3927, 4158, 4389, 4620, 4851, 5082, 5313, 5544, 5775, 6006, 6237, 6468, 6699, 6930, 7161, 7392, 7623, 7854, 8085, 8316, 8547, 8778, 9009, 9240, 9471, 9702, 9933, 10164, 10395, 10626, 10857, 11088, 11319, 11550, 11781, 12012, 12243, 12474, 12705, 12936, 13167, 13398, 13629, 13860, 14091, 14322, 14553, 14784, 15015, 15246, 15477, 15708, 15939, 16170, 16401, 16632, 16863, 17094, 17325, 17556, 17787, 18018, 18249, 18480, 18711, 18942, 19173, 19404, 19635, 19866, 20097, 20328, 20559, 20790, 21021, 21252, 21483, 21714, 21945, 22176, 22407, 22638, 22869, 23100, 23331, 23562, 23793, 24024, 24255, 24486, 24717, 24948, 25179, 25410, 25641, 25872, 26103, 26334, 26565, 26796, 27027, 27258, 27489, 27720, 27951, 28182, 28413, 28644, 28875, 29106, 29337, 29568, 29799, 30030, 30261, 30492, 30723, 30954, 31185, 31416, 31647, 31878, 32109, 32340, 32571, 32802, 33033, 33264, 33495, 33726, 33957, 34188, 34419, 34650, 34881, 35112, 35343, 35574, 35805, 36036, 36267, 36498, 36729, 36960, 37191, 37422, 37653, 37884, 38115, 38346, 38577, 38808, 39039, 39270, 39501, 39732, 39963, 40194, 40425, 40656, 40887, 41118, 41349, 41580, 41811, 42042, 42273, 42504, 42735, 42966, 43197, 43428, 43659, 43890, 44121, 44352, 44583, 44814, 45045, 45276, 45507, 45738, 45969, 46200, 46431, 46662, 46893, 47124, 47355, 47586, 47817, 48048, 48279, 48510, 48741, 48972, 49203, 49434, 49665, 49896, 50127, 50358, 50589, 50820, 51051, 51282, 51513, 51744, 51975, 52206, 52437, 52668, 52899, 53130, 53361, 53592, 53823, 54054, 54285, 54516, 54747, 54978, 55209, 55440, 55671, 55902, 56133, 56364, 56595, 56826, 57057, 57288, 57519, 57750, 57981, 58212, 58443, 58674, 58905, 59136, 59367, 59598, 59829, 60060, 60291, 60522, 60753, 60984, 61215, 61446, 61677, 61908, 62139, 62370, 62601, 62832, 63063, 63294, 63525, 63756, 63987, 64218, 64449, 64680, 64911, 65142, 65373, 65604, 65835, 66066, 66297, 66528, 66759, 66990, 67221, 67452, 67683, 67914, 68145, 68376, 68607, 68838, 69069, 69300, 69531, 69762, 69993, 70224, 70455, 70686, 70917, 71148, 71379, 71610, 71841, 72072, 72303, 72534, 72765, 72996, 73227, 73458, 73689, 73920, 74151, 74382, 74613, 74844, 75075, 75306, 75537, 75768, 75999, 76230, 76461, 76692, 76923, 77154, 77385, 77616, 77847, 78078, 78309, 78540, 78771, 79002, 79233, 79464, 79695, 79926, 80157, 80388, 80619, 80850, 81081, 81312, 81543, 81774, 82005, 82236, 82467, 82698, 82929, 83160, 83391, 83622, 83853, 84084, 84315, 84546, 84777, 85008, 85239, 85470, 85701, 85932, 86163, 86394, 86625, 86856, 87087, 87318, 87549, 87780, 88011, 88242, 88473, 88704, 88935, 89166, 89397, 89628, 89859, 90090, 90321, 90552, 90783, 91014, 91245, 91476, 91707, 91938, 92169, 92400, 92631, 92862, 93093, 93324, 93555, 93786, 94017, 94248, 94479, 94710, 94941, 95172, 95403, 95634, 95865, 96096, 96327, 96558, 96789, 97020, 97251, 97482, 97713, 97944, 98175, 98406, 98637, 98868, 99099, 99330, 99561, 99792
- There is a total of 432 numbers (up to 100000) that are divisible by 231.
- The sum of these numbers is 21604968.
- The arithmetic mean of these numbers is 50011.5.
How to find the numbers divisible by 231?
Finding all the numbers that can be divided by 231 is essentially the same as searching for the multiples of 231: if a number N is a multiple of 231, then 231 is a divisor of N.
Indeed, if we assume that N is a multiple of 231, this means there exists an integer k such that:
Conversely, the result of N divided by 231 is this same integer k (without any remainder):
From this we can see that, theoretically, there's an infinite quantity of multiples of 231 (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 231 less than 100000):
- 1 × 231 = 231
- 2 × 231 = 462
- 3 × 231 = 693
- ...
- 431 × 231 = 99561
- 432 × 231 = 99792