What 4 digit numbers have 3 and 13 as factors?

Answer 1

1014, 1053, 1092, 1131, 1170, 1209, 1248, 1287, 1326, 1365, 1404, 1443, 1482, 1521, 1560, 1599, 1638, 1677, 1716, 1755, 1794, 1833, 1872, 1911, 1950, 1989, 2028, 2067, 2106, 2145, 2184, 2223, 2262, 2301, 2340, 2379, 2418, 2457, 2496, 2535, 2574, 2613, 2652, 2691, 2730, 2769, 2808, 2847, 2886, 2925, 2964, 3003, 3042, 3081, 3120, 3159, 3198, 3237, 3276, 3315, 3354, 3393, 3432, 3471, 3510, 3549, 3588, 3627, 3666, 3705, 3744, 3783, 3822, 3861, 3900, 3939, 3978, 4017, 4056, 4095, 4134, 4173, 4212, 4251, 4290, 4329, 4368, 4407, 4446, 4485, 4524, 4563, 4602, 4641, 4680, 4719, 4758, 4797, 4836, 4875, 4914, 4953, 4992, 5031, 5070, 5109, 5148, 5187, 5226, 5265, 5304, 5343, 5382, 5421, 5460, 5499, 5538, 5577, 5616, 5655, 5694, 5733, 5772, 5811, 5850, 5889, 5928, 5967, 6006, 6045, 6084, 6123, 6162, 6201, 6240, 6279, 6318, 6357, 6396, 6435, 6474, 6513, 6552, 6591, 6630, 6669, 6708, 6747, 6786, 6825, 6864, 6903, 6942, 6981, 7020, 7059, 7098, 7137, 7176, 7215, 7254, 7293, 7332, 7371, 7410, 7449, 7488, 7527, 7566, 7605, 7644, 7683, 7722, 7761, 7800, 7839, 7878, 7917, 7956, 7995, 8034, 8073, 8112, 8151, 8190, 8229, 8268, 8307, 8346, 8385, 8424, 8463, 8502, 8541, 8580, 8619, 8658, 8697, 8736, 8775, 8814, 8853, 8892, 8931, 8970, 9009, 9048, 9087, 9126, 9165, 9204, 9243, 9282, 9321, 9360, 9399, 9438, 9477, 9516, 9555, 9594, 9633, 9672, 9711, 9750, 9789, 9828, 9867, 9906, 9945, 9984

All numbers that have 3 and 13 as factors are multiples of the LCM of 3 and 13 which is 39.

The 4 digit numbers are 1000 to 9999 and of these, the multiples of 39 are:

1000 ÷ 39 = 2525/39 ⇒ first multiple of 39 greater than or equal to 1000 is 26 x 39 = 1014

9999 ÷ 39= 25615/39 ⇒ last multiple of 39 less than or equal to 9999 is 256 x 39 = 9984

Thus the multiples from 26 to 256 of 39 are the 4 digit numbers with 3 and 13 as factors.