Problem on Division algorithm
Number Theory
Level
3
Let the Greatest Common Divisor of 126 and 658 be "d". Then find value of x such that : d=126x +658y.(y belongs to integers)
The answer is 21.
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By Division Algorithm,
658=5(126)+28 .....................(1)
126=4(28)+14 ......................(2)
28=2(14)+0
So, G.C.D(i.e. d)=14
From (2),
14=126 - 4(28)
So, 14 =126 -4(658 -5(126)) (From (2))
So, 14(i.e. d)=21(126) -5(658)
So, x=21