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Math Help - Eulcidean Algorithim for GCD

  1. #1
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    Eulcidean Algorithim for GCD

    Find the GCD for 198 and 765

    I got as far as 765= 3 \times 198   +171
    I'm not sure what to do for the next step.
    Last edited by kamui; May 2nd 2013 at 01:05 PM.
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  2. #2
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    Re: Eulcidean Algorithim for GCD

    The next step is: 198 = 1 x 171 + 27. For each new step, you take the two rightmost numbers from the previous step.
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  3. #3
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    Re: Eulcidean Algorithim for GCD

    ello, kamui!

    Find the GCD for 198 and 765

    I got as far as: 765\:=\: 3 \times 198   +171

    I'm not sure what to do for the next step.

    Then I guess you didn't really learn the Euclidean Algorithm.

    1. Divide the larger number by the smaller.

    2. Divide the divisor by the remainder.

    3. Repeat step 2 until a zero remainder is achieved.

    4. The GCD is the last divisor.


    So we have:

    . . \begin{array}{ccccc}765 \div 198 &=& 3 & \text{rem.}171 \\ 198 \div 171 &=& 1 & \text{rem.}27 \\ 171 \div 27 &=& 6 & \text{rem.}9 \\ 27 \div {\color{red}9} &=& 3 & \text{rem.}0 \end{array}


    Therefore: . \text{GCD}(198,765) \:=\:9
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