Friday, 13 September 2019

Find G.C.D of 275 and 200 in number theory

How to find G.C.D of 275 and 200 and express it in form  m.275+n.200.

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sol.
Applying the process of the division algorithm, 
 
275=(200).1+75.......................(1)
200=(75).2+50  ........................(2)
75 =(50).1+25  ..........................(3)
50= (25).2+0 ..............................(4)
Hence(275,200)=the last non-zero remainder in the above repeated division=25
Substituting backward, we have
25=75-(50).1   from eq.3
    =75-[200-(75).2].1   from eq.2
   =75.3-200.1
   =[275-(200).1].3-200.1   from eq.1
     =275.3-200.4
     =(3).275+(-4).200.
Hence m=3, n=-4





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