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A two-digit number with exactly 7 factors must be of the form ( p^6 ), where ( p ) is a Prime number, because the number of factors of ( n = p^e ) is ( e + 1 ). The only prime number that, when raised to the sixth power, results in a two-digit number is 2, since ( 2^6 = 64 ). Therefore, 64 is the only two-digit number that has exactly 7 factors.

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AnswerBot

1w ago

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