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Prime factors

This topic has 1 expert reply and 1 member reply
richs_ca Junior | Next Rank: 30 Posts Default Avatar
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Prime factors

Post Sat May 03, 2008 10:33 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    For all integers p, <<p>> is the product of p's distinct prime factors. What is the greatest common factor of <<24>> and <<54>>?

    a. <<2>>
    b. <<3>>
    c. <<8>>
    d. <<12>>
    e <<14>>

    How do I figure this out?

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    Post Sat May 03, 2008 10:56 am
    richs_ca wrote:
    For all integers p, <<p>> is the product of p's distinct prime factors. What is the greatest common factor of <<24>> and <<54>>?

    a. <<2>>
    b. <<3>>
    c. <<8>>
    d. <<12>>
    e <<14>>

    How do I figure this out?
    Break it down!

    54 = 2 * 27 = 2*3*3*3
    So, the distinct prime factors of 54 are 2 and 3, and <<54>> is 2*3 = 6

    24 = 2*12 = 2*2*2*3
    So, <<24>> is also 2*3 = 6

    Therefore, the GCF of <<24>> and <<54>> is 6.

    Now, the answers are also in <<x>> form, so we want to pick a choice that's made up of 2s and 3s.

    a) no 3
    b) no 2
    c) no 3
    d) only 2s and 3s! Winner!
    e) no 3

    choose (d).

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    simplyjat Master | Next Rank: 500 Posts
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    Post Sat May 03, 2008 10:57 am
    The answer is d. <<12>>

    So you know the definition of <<p>>.
    To find <<24>>, break 24 in prime factors. 24 = 2*2*2*3. 2 and 3 are the only distinct prime factors and there product is 6. So <<24>> = 6
    Similarly for <<54>>, 54 = 2*3*3*3 and <<54>> = 6

    LCM of 6 & 6 is 6. So if the answers were provided in simple integers the answer would be 6. But the answer is a multiple of 6 or should only contain 2 and 3 as the only prime factors.

    Looking at the answers <<12>> is the only answer that matches the criteria.

    _________________
    simplyjat

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