What is a four digit number divisible by 4 and 9?

Answer 1

Any number to be divisible by 4 and 9 must be a multiple of their lowest common multiple; lcm(4, 9) = 36. Thus:

First 4 digit number is 1000 → 1000 ÷ 36 = 27 7/9 → first multiple of 36 which is a 4 digit number is 28 × 36 (= 1008);

Last 4 digit number is 9999 → 9999 ÷ 36 = 277 3/4 → last multiple of 36 which is a 4 digit number is 277 × 36 (= 9972);

Thus all multiples of 36 between 28 and 277 (inclusive) are four digit numbers divisible by both 4 and 9, namely:

1008, 1044, 1080, 1116, 1152, 1188, 1224, 1260, 1296, 1332, 1368, 1404, 1440, 1476, 1512, 1548, 1584, 1620, 1656, 1692, 1728, 1764, 1800, 1836, 1872, 1908, 1944, 1980, 2016, 2052, 2088, 2124, 2160, 2196, 2232, 2268, 2304, 2340, 2376, 2412, 2448, 2484, 2520, 2556, 2592, 2628, 2664, 2700, 2736, 2772, 2808, 2844, 2880, 2916, 2952, 2988, 3024, 3060, 3096, 3132, 3168, 3204, 3240, 3276, 3312, 3348, 3384, 3420, 3456, 3492, 3528, 3564, 3600, 3636, 3672, 3708, 3744, 3780, 3816, 3852, 3888, 3924, 3960, 3996, 4032, 4068, 4104, 4140, 4176, 4212, 4248, 4284, 4320, 4356, 4392, 4428, 4464, 4500, 4536, 4572, 4608, 4644, 4680, 4716, 4752, 4788, 4824, 4860, 4896, 4932, 4968, 5004, 5040, 5076, 5112, 5148, 5184, 5220, 5256, 5292, 5328, 5364, 5400, 5436, 5472, 5508, 5544, 5580, 5616, 5652, 5688, 5724, 5760, 5796, 5832, 5868, 5904, 5940, 5976, 6012, 6048, 6084, 6120, 6156, 6192, 6228, 6264, 6300, 6336, 6372, 6408, 6444, 6480, 6516, 6552, 6588, 6624, 6660, 6696, 6732, 6768, 6804, 6840, 6876, 6912, 6948, 6984, 7020, 7056, 7092, 7128, 7164, 7200, 7236, 7272, 7308, 7344, 7380, 7416, 7452, 7488, 7524, 7560, 7596, 7632, 7668, 7704, 7740, 7776, 7812, 7848, 7884, 7920, 7956, 7992, 8028, 8064, 8100, 8136, 8172, 8208, 8244, 8280, 8316, 8352, 8388, 8424, 8460, 8496, 8532, 8568, 8604, 8640, 8676, 8712, 8748, 8784, 8820, 8856, 8892, 8928, 8964, 9000, 9036, 9072, 9108, 9144, 9180, 9216, 9252, 9288, 9324, 9360, 9396, 9432, 9468, 9504, 9540, 9576, 9612, 9648, 9684, 9720, 9756, 9792, 9828, 9864, 9900, 9936, 9972

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