OK, so maybe I'm making a fool of myself; it won't be the first time. Assume positive integers, and assume that 1 (one) is one of the factors. Also assume that any factor is used only once. If factors can be used any number of times then any number answers the question (seven ones and the number). The smallest number with 8 distinct factors is 510510. If you do not count 1 as a factor, the smallest such number is 9699690. In order, the factors would be 1, 2, 3, 5, 7, 11, 13, 17, (19).
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