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1. Least number of factors giving 51/2010 ●●●●○ 100 ptsFind the least positive integer $n$ for which there exists a set $\{s_1, s_2, \ldots, s_n\}$ consisting of $n$ distinct positive integers such that $$\left(1-\frac{1}{s_1}\right)\left(1-\frac{1}{s_2}\right)\cdots\left(1-\frac{1}{s_n}\right)=\frac{51}{2010}.$$