Results 1 to 4 of 4

Math Help - Another GCD using Euclid's Algorithm

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    17

    Talking Another GCD using Euclid's Algorithm

    Here is another problem that I think I may have gotten right. Can someone help me? What do you get?

    (85,65)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    \begin{array}{rcl} 85 & = & (1)({\color{red}65}) + {\color{blue}20} \\ {\color{red}65} & = & (3)({\color{blue}20}) + {\color{magenta}5} \\ {\color{blue}20}  & = & 4({\color{magenta}5}) + 0 \end{array}

    So by Euclid's algorithm, (85, 65) = ... = ... ? Can you conclude?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2008
    Posts
    17
    Sorry I forgot to mention that I have to express it as ma + nb
    Follow Math Help Forum on Facebook and Google+

  4. #4
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    Ok well, we can see that (85,65) = (65,20) = (20,5) = (5,0) = 5.

    So, going with what I did in my earlier post:
    \begin{array}{rcll}5 & = & 65 - 3(20) & \text{Rearranged the second line} \\ 5 & = & 65 - 3 \left(85 - 65\right) & \text{Used the first line (rearranged)} \\ & \vdots & \end{array}

    Just a matter of simplifying.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Euclid Algorithm
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: January 15th 2012, 12:32 PM
  2. Euclid's Algorithm
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: March 29th 2009, 05:54 AM
  3. Finding GCD using Euclid's algorithm
    Posted in the Number Theory Forum
    Replies: 15
    Last Post: September 23rd 2008, 07:45 PM
  4. Euclid's algorithm
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: August 3rd 2008, 06:18 AM
  5. Euclid Algorithm
    Posted in the Number Theory Forum
    Replies: 5
    Last Post: April 10th 2008, 06:28 AM

Search Tags


/mathhelpforum @mathhelpforum