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Math Help - GCF factoring Question

  1. #1
    Member cmf0106's Avatar
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    Talking GCF factoring Question

    Regarding GCF factoring, can the same answer be derived from multiple number sets? Specifically fin the following problem:

    40a^5x+80a^5y-120a^5z & its answer 40a^5(x + 2y - 3z)

    40 obviously is the GCF and goes into all three numbers. But what if one doesn't realize this initially and decides to approach it as such?

    pulling out the terms
     40a^5x = 2^2*10
    80a^5y=2^4*5
    -120a^5z= 2^3*15

    then finding the lowest power of each variable and number. Will one still arrive at the same answer as if they used 40 as the GCF?
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  2. #2
    A riddle wrapped in an enigma
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    This is true.

    40=2^3\cdot5

    80=2^4\cdot5

    120=2^3\cdot3\cdot5

    Use all the common factors with the least exponent.

    Thus, we have 2^3\cdot5=40

    Do the same for the variables. Find the common variables and use the least exponent.
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  3. #3
    Member cmf0106's Avatar
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    Yikes, you changed yours up a little bit in your example

    Instead of what I used, 2^2 * 10 = 40 for the first term you used 2^3 * 5 was. So is answer is already wrong at this point, going with 2^2 * 10 = 40? If so how can I avoid future problems such as this?
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by cmf0106 View Post
    Yikes, you changed yours up a little bit in your example

    Instead of what I used, 2^2 * 10 = 40 for the first term you used 2^3 * 5 was. So is answer is already wrong at this point, going with 2^2 * 10 = 40? If so how can I avoid future problems such as this?

    You should factor your numbers into the product of primes.

    40=2^3\cdot5, otherwise you may miss an exponent. You were lucky this time since you already had a 2^3 as a factor of 120.
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  5. #5
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    Quote Originally Posted by cmf0106 View Post
    Yikes, you changed yours up a little bit in your example

    Instead of what I used, 2^2 * 10 = 40 for the first term you used 2^3 * 5 was. So is answer is already wrong at this point, going with 2^2 * 10 = 40? If so how can I avoid future problems such as this?
    When factoring numbers to find the GCF, you should factor everything completely into powers of prime numbers. 10 is not prime, because 10=2\cdot5, but 2 and 5 are both prime. Once you have factored completely, then you can take the common factors, and their product will be your greatest common factor.
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  6. #6
    A riddle wrapped in an enigma
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    Could not have said it better myself.
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