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Math Help - divisors

  1. #1
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    divisors

    Could you please help me with this question:

    Find all positive integers N such that the product 2005 *N has exactly six divisors.
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  2. #2
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    5 * 401 = 2005

    5*401*2*2*2*2 = 2005*16
    5*401*2*2*2*3 = 2005*24
    5*401*2*2*2*5 = 2005*60

    this could go on forever. Ther are infinites N's where this would work.
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  3. #3
    hpe
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    Corrected solution

    Quote Originally Posted by Math Help
    5 * 401 = 2005

    5*401*2*2*2*2 = 2005*16
    5*401*2*2*2*3 = 2005*24
    5*401*2*2*2*5 = 2005*60

    this could go on forever. Ther are infinites N's where this would work.
    2005*16 has too many divisors, namely 1,2,4,8,10,16,20,...

    Try M = 5: Then 1, 5, 25, 401, 2005, 10025 are the only divisors of 2005*5.
    M = 401 also works.
    If M has any prime factor other than 5 or 401, let's say p, there will be at least seven divisors: 1, 5, 401, p, 5p, 401p, 2005p.

    If M is a power of 5 or has divisors 5 and 401, there will also be too many divisors.
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  4. #4
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    Thanks for the help

    Thanks for the help
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  5. #5
    vingta
    Guest

    Angry Cheat!!

    Cheater!!!!!
    Your suppose to do the Euler questions by yourself. Just look at thus website, http://www.amt.edu.au/mcya.html,
    You CHEAT!!!!
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