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Homework Help: How can i prove that a multiple of 4 is a multiple of 12?

  1. Mar 29, 2005 #1
    How can i prove that a multiple of 4 is a multiple of 12?
     
  2. jcsd
  3. Mar 29, 2005 #2

    xanthym

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    You can't ... because it's NOT true.
    Example:
    (2)*(4)=(8) is NOT a {Multiple of (12)}

    However, you can prove that a {Multiple of (12)} is a {Multiple of (4)}. Begin by factoring (12):
    (12) = (4)*(3)
    Now consider the integer "k" multiple of (12) given by (12)*k, where {k = 1, 2, 3, ...}:
    {"k" Multiple of (12)} = (12)*k = {(4)*(3)}*k = (4)*{(3)*k} = (4)*m
    where "m" is a positive integer. Thus:
    {Multiple of (12)} IS A {Multiple of (4)}


    ~~
     
    Last edited: Mar 29, 2005
  4. Mar 29, 2005 #3

    HallsofIvy

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    It is true that a multiple of 12 is a multiple of 4- just the opposite of the original post. That's true because "multiple of 12" MEANS "12 times some integer". If x is a multiple of 12, then x= 12n for some integer n. "Multiple of 4" MEANS "4 times some integer". Of course, if x is a multiple of 12 then x= 12n= 4(3n) so that x is 4 times the integer 3n: a multiple of 4.
     
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