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Thread: Largest factor of consecutive natural numbers

  1. #1
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    Post Largest factor of consecutive natural numbers

    1) The largest Number, which exactly divides the product of any three consecutive integers is ...

    (a) 2 (b) 3 (c) 6 (d) 12
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    MHF Contributor ebaines's Avatar
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    Re: Largest factor of consecutive natural numbers

    Think about it ... for any three consecutive positive integers at least one must be even, and at least one must be a multiple of 3. What does that tell you about the largest number that must be divisible into the product of three consecutive positive integers?
    Last edited by ebaines; Aug 6th 2013 at 09:47 AM.
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    Re: Largest factor of consecutive natural numbers

    One "product of three consecutive integers" is 1(2)(3). Another is 2(3)(4). What is the largest integer that divides both of those.
    Of course, it remains to be shown that this integer divides any factor of three consecutive integers. What is true of every other integer? What is true of every third integer?
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