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Q: What is the third smallest natural number that has exactly four distinct positive factors?

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The smallest number that has exactly eight factors is 24. The factors of 1,2,3,4,6,8,12, and 24

A positive integer with exactly two distinct factors.

what is the smallest positive integer that has four different prime factors

How about: 210

The smallest number with exactly eight factors is 24.

24edit: nonethe smallest number with 12 distinct factors would be2*3*5*7*11*13*17*19*23*29*31*37>>100

12

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