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Math Help - prime factorization and factors

  1. #1
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    prime factorization and factors

    What is the smallest whole number that has exactly 16 factors?


    i think i understand this type of problem, but i am looking for confirmation...is 120 the correct answer?
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by ihavvaquestion View Post
    What is the smallest whole number that has exactly 16 factors?


    i think i understand this type of problem, but i am looking for confirmation...is 120 the correct answer?
    Explain why you think 120 is the correct answer.
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  3. #3
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    chip i think its because in terms of prime factorization a number that has exactly 16 factors has to look like one of the following:

    16*1 = p^15
    4*4 = p^3*q^3
    2*2*2*2 = pqrs
    4*2*2 = p^3*qr
    8*2= p^7*q

    looking at these i checked them out and using the smallest primes i figured the first and last ones to be way too big, but

    2^3*3^3 = 216
    2*3*5*7 = 210
    2^3*3*5 = 120

    so 120 must be the smallest whole number that has exactly 16 factors...right?
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