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Thread: Length of 3

  1. #1
    Super Member harpazo's Avatar
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    Length of 3

    For any positive integer n, n > 1, the "length" of n is the number of positive primes (not necessarily distinct) whose product is n. For example, the length of 50 is 3 since 50 = (2)(5)(5). Given this information, which of the following integers has a length of 3?

    A. 3
    B. 15
    C. 60
    D. 64
    E. 105

    I said 15 2 2 = 30 2 = 60.
    The correct answer is 105. Why is my answer incorrect?
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: Length of 3

    Quote Originally Posted by harpazo View Post
    For any positive integer n, n > 1, the "length" of n is the number of positive primes (not necessarily distinct) whose product is n. For example, the length of 50 is 3 since 50 = (2)(5)(5). Given this information, which of the following integers has a length of 3?

    A. 3
    B. 15
    C. 60
    D. 64
    E. 105

    I said 15 2 2 = 30 2 = 60.
    The correct answer is 105. Why is my answer incorrect?
    60 doesn't work because it factors as 2^2 x 3 x 5. You need them to be prime factors. 15 is not prime.

    Now 105 = 5^3 = 5 x 5 x 5 so this would have a length of 3.

    -Dan
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    Re: Length of 3

    Quote Originally Posted by harpazo View Post
    For any positive integer n, n > 1, the "length" of n is the number of positive primes (not necessarily distinct) whose product is n. For example, the length of 50 is 3 since 50 = (2)(5)(5). Given this information, which of the following integers has a length of 3?

    A. 3
    B. 15
    C. 60
    D. 64
    E. 105

    I said 15 • 2 • 2 = 30 • 2 = 60.
    The correct answer is 105. Why is my answer incorrect?
    Look at this tool. Using that tool we see that the length of 168 is five (3+1+1=5)
    You can simple 168 to any other number, hit enter then proceed. Explore that site for other goodies.
    Thanks from topsquark
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  4. #4
    Super Member harpazo's Avatar
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    Re: Length of 3

    Quote Originally Posted by topsquark View Post
    60 doesn't work because it factors as 2^2 x 3 x 5. You need them to be prime factors. 15 is not prime.

    Now 105 = 5^3 = 5 x 5 x 5 so this would have a length of 3.

    -Dan
    Isn't 5^3 = 125?
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  5. #5
    Super Member harpazo's Avatar
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    Re: Length of 3

    Quote Originally Posted by Plato View Post
    Look at this tool. Using that tool we see that the length of 168 is five (3+1+1=5)
    You can simple 168 to any other number, hit enter then proceed. Explore that site for other goodies.
    I use Wolfram occasionally.
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    Re: Length of 3

    Quote Originally Posted by harpazo View Post
    I use Wolfram occasionally.
    If I were you, given your poor foundation in basic mathematics, I would use it all the time.
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  7. #7
    Super Member harpazo's Avatar
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    Re: Length of 3

    Quote Originally Posted by Plato View Post
    If I were you, given your poor foundation in basic mathematics, I would use it all the time.
    I'll try using Wolfram as much as possible. I am not in a math class. No need to stress it out. I find math interestingly fun to play with.
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  8. #8
    Super Member harpazo's Avatar
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    Re: Length of 3

    Quote Originally Posted by topsquark View Post
    60 doesn't work because it factors as 2^2 x 3 x 5. You need them to be prime factors. 15 is not prime.

    Now 105 = 5^3 = 5 x 5 x 5 so this would have a length of 3.

    -Dan
    For example, does 8 have a length of 3 considering that 2^3 = 2 • 2 • 2?
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