Which 4 digit number can be divided by 6 and 9?

Answer 1

To be divided by 6 and 9, the number must be divisible by the lcm of 6 and 9 = 18.

The solution is 4 digit multiples of 18:

1000 ÷ 18 = 555/9 ⇒ first 4 digit multiple of 18 is 18 x 56 = 1008

9999 ÷ 18 = 5551/2 ⇒ last 4 digit multiple of 18 is 18 x 555 = 9990

Which means the 500 4-digit numbers divisible by 6 and 9 are:

1008, 1026, 1044, 1062, 1080, 1098, 1116, 1134, 1152, 1170, 1188, 1206, 1224, 1242, 1260, 1278, 1296, 1314, 1332, 1350, 1368, 1386, 1404, 1422, 1440, 1458, 1476, 1494, 1512, 1530, 1548, 1566, 1584, 1602, 1620, 1638, 1656, 1674, 1692, 1710, 1728, 1746, 1764, 1782, 1800, 1818, 1836, 1854, 1872, 1890, 1908, 1926, 1944, 1962, 1980, 1998, 2016, 2034, 2052, 2070, 2088, 2106, 2124, 2142, 2160, 2178, 2196, 2214, 2232, 2250, 2268, 2286, 2304, 2322, 2340, 2358, 2376, 2394, 2412, 2430, 2448, 2466, 2484, 2502, 2520, 2538, 2556, 2574, 2592, 2610, 2628, 2646, 2664, 2682, 2700, 2718, 2736, 2754, 2772, 2790, 2808, 2826, 2844, 2862, 2880, 2898, 2916, 2934, 2952, 2970, 2988, 3006, 3024, 3042, 3060, 3078, 3096, 3114, 3132, 3150, 3168, 3186, 3204, 3222, 3240, 3258, 3276, 3294, 3312, 3330, 3348, 3366, 3384, 3402, 3420, 3438, 3456, 3474, 3492, 3510, 3528, 3546, 3564, 3582, 3600, 3618, 3636, 3654, 3672, 3690, 3708, 3726, 3744, 3762, 3780, 3798, 3816, 3834, 3852, 3870, 3888, 3906, 3924, 3942, 3960, 3978, 3996, 4014, 4032, 4050, 4068, 4086, 4104, 4122, 4140, 4158, 4176, 4194, 4212, 4230, 4248, 4266, 4284, 4302, 4320, 4338, 4356, 4374, 4392, 4410, 4428, 4446, 4464, 4482, 4500, 4518, 4536, 4554, 4572, 4590, 4608, 4626, 4644, 4662, 4680, 4698, 4716, 4734, 4752, 4770, 4788, 4806, 4824, 4842, 4860, 4878, 4896, 4914, 4932, 4950, 4968, 4986, 5004, 5022, 5040, 5058, 5076, 5094, 5112, 5130, 5148, 5166, 5184, 5202, 5220, 5238, 5256, 5274, 5292, 5310, 5328, 5346, 5364, 5382, 5400, 5418, 5436, 5454, 5472, 5490, 5508, 5526, 5544, 5562, 5580, 5598, 5616, 5634, 5652, 5670, 5688, 5706, 5724, 5742, 5760, 5778, 5796, 5814, 5832, 5850, 5868, 5886, 5904, 5922, 5940, 5958, 5976, 5994, 6012, 6030, 6048, 6066, 6084, 6102, 6120, 6138, 6156, 6174, 6192, 6210, 6228, 6246, 6264, 6282, 6300, 6318, 6336, 6354, 6372, 6390, 6408, 6426, 6444, 6462, 6480, 6498, 6516, 6534, 6552, 6570, 6588, 6606, 6624, 6642, 6660, 6678, 6696, 6714, 6732, 6750, 6768, 6786, 6804, 6822, 6840, 6858, 6876, 6894, 6912, 6930, 6948, 6966, 6984, 7002, 7020, 7038, 7056, 7074, 7092, 7110, 7128, 7146, 7164, 7182, 7200, 7218, 7236, 7254, 7272, 7290, 7308, 7326, 7344, 7362, 7380, 7398, 7416, 7434, 7452, 7470, 7488, 7506, 7524, 7542, 7560, 7578, 7596, 7614, 7632, 7650, 7668, 7686, 7704, 7722, 7740, 7758, 7776, 7794, 7812, 7830, 7848, 7866, 7884, 7902, 7920, 7938, 7956, 7974, 7992, 8010, 8028, 8046, 8064, 8082, 8100, 8118, 8136, 8154, 8172, 8190, 8208, 8226, 8244, 8262, 8280, 8298, 8316, 8334, 8352, 8370, 8388, 8406, 8424, 8442, 8460, 8478, 8496, 8514, 8532, 8550, 8568, 8586, 8604, 8622, 8640, 8658, 8676, 8694, 8712, 8730, 8748, 8766, 8784, 8802, 8820, 8838, 8856, 8874, 8892, 8910, 8928, 8946, 8964, 8982, 9000, 9018, 9036, 9054, 9072, 9090, 9108, 9126, 9144, 9162, 9180, 9198, 9216, 9234, 9252, 9270, 9288, 9306, 9324, 9342, 9360, 9378, 9396, 9414, 9432, 9450, 9468, 9486, 9504, 9522, 9540, 9558, 9576, 9594, 9612, 9630, 9648, 9666, 9684, 9702, 9720, 9738, 9756, 9774, 9792, 9810, 9828, 9846, 9864, 9882, 9900, 9918, 9936, 9954, 9972, 9990