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3

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

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4 and 9

A positive integer with exactly two distinct factors.

12

30

I think that it is 4

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4 and 9

230

230

Among positive integers, 6

A positive integer with exactly two distinct factors.

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

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

The smallest number with exactly eight factors is 24.

4096 is the smallest number with exactly 13 factors. (Including 1 and itself as factors).192 is the smallest number with exactly 13 properfactors, (excluding the number itself).120 is the smallest number with at least 13 factors (it has 16 factors)To find the smallest number with exactly N factors (for example, N=12):Factor N into primes, (for example, 12= 2*2*3Subtract 1 from each of the prime factors (for example, 1,1,2)Sort them by largest first (for example, 2,1,1)Raise successive prime numbers to these powers (for example, 2^2,3^1,5^1)Multiply these together (for example: 4*3*5 = 60; 60 is the smallest number with exactly 12 factors).

How about: 210

Prime squares have three factors. There are 11 of them in that range.

192