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Thread: Greatest Common Divisor

  1. #1
    Super Member harpazo's Avatar
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    Greatest Common Divisor

    Which of the following CANNOT be the greatest common divisor of the two positive integers x and y?

    A. 1
    B. x
    C. y
    D. x - y
    E. x + y

    I do not understand exactly what this question is asking?
    The answer is choice E. I do not understand why E is the answer. Can someone state this question another way?
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  2. #2
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    Re: Greatest Common Divisor

    Quote Originally Posted by harpazo View Post
    Which of the following CANNOT be the greatest common divisor of the two positive integers x and y?
    A. 1
    B. x
    C. y
    D. x - y
    E. x + y
    I do not understand exactly what this question is asking?
    The answer is choice E. I do not understand why E is the answer. Can someone state this question another way?
    To find the $GCF(x,y)$ write down the prime factorization of each. Then list the common factors with the least power present.
    EX: $x=2^5\cdot3^5\cdot 5^3\cdot 7^4\cdot 11^5~\& ~y=2^3\cdot 7^5\cdot 11^8\cdot 13^5\cdot$ $GCF(x,y)=2^3\cdot7^4\cdot 11^5$

    NOTE $GCD(x,y)\le\min\{x,y\}$
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  3. #3
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    Re: Greatest Common Divisor

    It's much simpler than that. Because x and y are "two positive integers", x+ y is larger than either x or y so cannot be a divisor of either one, much less a "common" divisor!
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  4. #4
    Super Member harpazo's Avatar
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    Re: Greatest Common Divisor

    Quote Originally Posted by Plato View Post
    To find the $GCF(x,y)$ write down the prime factorization of each. Then list the common factors with the least power present.
    EX: $x=2^5\cdot3^5\cdot 5^3\cdot 7^4\cdot 11^5~\& ~y=2^3\cdot 7^5\cdot 11^8\cdot 13^5\cdot$ $GCF(x,y)=2^3\cdot7^4\cdot 11^5$

    NOTE $GCD(x,y)\le\min\{x,y\}$
    Your reply is too mathematical. I did not major in math.
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  5. #5
    Super Member harpazo's Avatar
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    Re: Greatest Common Divisor

    Quote Originally Posted by HallsofIvy View Post
    It's much simpler than that. Because x and y are "two positive integers", x+ y is larger than either x or y so cannot be a divisor of either one, much less a "common" divisor!
    This makes a little more sense than Plato's reply.
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