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Since 5 is not a factor, it cannot be 15, whose digits add up to 6. The easiest way is to look at the multiples of 3.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, ... , 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, ... , 201, 204, 207, 210, 213, 216, 219, 222, 225, 228, 231, ... , 300, 303, 306, 309, 312, 315, 318, 321, ... , 402, 405, 408, 411, ... , 501, 504, 507, 510, ... , 1002, 1005, 1008, 1011, 1014, 1017, 1020, 1023, ...

Other numbers whose digits add up to 6 are 24, 33, 42, 51, 60, 105, 114, 123, 132, 141, 150, 204, 213, 222, 231, 303, 312, 321, 402, 411, 501, 510, 1005, 1014, and 1023. Some of these have 5 as a factor, so you must eliminate 60, 105, 150, 510, and 1005, but there are still many numbers that fit this condition, and there are more that were not listed here.

If the number has only four factors, 1, 3, the one that is not 5, and itself, that eliminates more of the possible answers. Some of the remaining possibilities are:

33 = 3 x 11

51 = 3 x 17

123 = 3 x 41

141 = 3 x 47

213 = 3 x 71

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Q: What number whose digits add up to 6 has one factor that is 3 but does not have a factor that is 5?
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