What four digit number is divisible by 3 and 5 but not 4?

Answer 1

There are a great number of them (450 in fact).

All multiples of the lowest common multiple of 3 and 5 (which is 15) which are not multiples of the lcm of 3, 4 and 5 (which is 60) will solve the problem, thus any of the four digit numbers, namely:

1005, 1035, 1050, 1065, 1095, 1110, 1125, 1155, 1170, 1185, 1215, 1230, 1245, 1275, 1290, 1305, 1335, 1350, 1365, 1395, 1410, 1425, 1455, 1470, 1485, 1515, 1530, 1545, 1575, 1590, 1605, 1635, 1650, 1665, 1695, 1710, 1725, 1755, 1770, 1785, 1815, 1830, 1845, 1875, 1890, 1905, 1935, 1950, 1965, 1995, 2010, 2025, 2055, 2070, 2085, 2115, 2130, 2145, 2175, 2190, 2205, 2235, 2250, 2265, 2295, 2310, 2325, 2355, 2370, 2385, 2415, 2430, 2445, 2475, 2490, 2505, 2535, 2550, 2565, 2595, 2610, 2625, 2655, 2670, 2685, 2715, 2730, 2745, 2775, 2790, 2805, 2835, 2850, 2865, 2895, 2910, 2925, 2955, 2970, 2985, 3015, 3030, 3045, 3075, 3090, 3105, 3135, 3150, 3165, 3195, 3210, 3225, 3255, 3270, 3285, 3315, 3330, 3345, 3375, 3390, 3405, 3435, 3450, 3465, 3495, 3510, 3525, 3555, 3570, 3585, 3615, 3630, 3645, 3675, 3690, 3705, 3735, 3750, 3765, 3795, 3810, 3825, 3855, 3870, 3885, 3915, 3930, 3945, 3975, 3990, 4005, 4035, 4050, 4065, 4095, 4110, 4125, 4155, 4170, 4185, 4215, 4230, 4245, 4275, 4290, 4305, 4335, 4350, 4365, 4395, 4410, 4425, 4455, 4470, 4485, 4515, 4530, 4545, 4575, 4590, 4605, 4635, 4650, 4665, 4695, 4710, 4725, 4755, 4770, 4785, 4815, 4830, 4845, 4875, 4890, 4905, 4935, 4950, 4965, 4995, 5010, 5025, 5055, 5070, 5085, 5115, 5130, 5145, 5175, 5190, 5205, 5235, 5250, 5265, 5295, 5310, 5325, 5355, 5370, 5385, 5415, 5430, 5445, 5475, 5490, 5505, 5535, 5550, 5565, 5595, 5610, 5625, 5655, 5670, 5685, 5715, 5730, 5745, 5775, 5790, 5805, 5835, 5850, 5865, 5895, 5910, 5925, 5955, 5970, 5985, 6015, 6030, 6045, 6075, 6090, 6105, 6135, 6150, 6165, 6195, 6210, 6225, 6255, 6270, 6285, 6315, 6330, 6345, 6375, 6390, 6405, 6435, 6450, 6465, 6495, 6510, 6525, 6555, 6570, 6585, 6615, 6630, 6645, 6675, 6690, 6705, 6735, 6750, 6765, 6795, 6810, 6825, 6855, 6870, 6885, 6915, 6930, 6945, 6975, 6990, 7005, 7035, 7050, 7065, 7095, 7110, 7125, 7155, 7170, 7185, 7215, 7230, 7245, 7275, 7290, 7305, 7335, 7350, 7365, 7395, 7410, 7425, 7455, 7470, 7485, 7515, 7530, 7545, 7575, 7590, 7605, 7635, 7650, 7665, 7695, 7710, 7725, 7755, 7770, 7785, 7815, 7830, 7845, 7875, 7890, 7905, 7935, 7950, 7965, 7995, 8010, 8025, 8055, 8070, 8085, 8115, 8130, 8145, 8175, 8190, 8205, 8235, 8250, 8265, 8295, 8310, 8325, 8355, 8370, 8385, 8415, 8430, 8445, 8475, 8490, 8505, 8535, 8550, 8565, 8595, 8610, 8625, 8655, 8670, 8685, 8715, 8730, 8745, 8775, 8790, 8805, 8835, 8850, 8865, 8895, 8910, 8925, 8955, 8970, 8985, 9015, 9030, 9045, 9075, 9090, 9105, 9135, 9150, 9165, 9195, 9210, 9225, 9255, 9270, 9285, 9315, 9330, 9345, 9375, 9390, 9405, 9435, 9450, 9465, 9495, 9510, 9525, 9555, 9570, 9585, 9615, 9630, 9645, 9675, 9690, 9705, 9735, 9750, 9765, 9795, 9810, 9825, 9855, 9870, 9885, 9915, 9930, 9945, 9975, 9990

take your pick.