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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*3

Subtract 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).

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11y ago

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