Answer:
{0, 1, 2, 4, 5, 6, 8}
Explanation:
120/230 = 12/23
121/231 = 11/21
122/232 = 61/116
123/233 -- not reducible
124/234 = 62/117
125/235 = 25/47
126/236 = 63/118
127/237 -- not reducible
128/238 = 64/119
129/239 -- not reducible
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All even digits will make the fraction reducible, as will the digit 5. Then the digits we're not sure of are 1, 3, 7, 9. Appending 1 to the given numbers makes them divisible by 11, so that digit is included in our list.
Ending digits 3, 7, 9 result in fractions that are not reducible. (Numbers 127, 233, and 239 are prime numbers.)