Euclidean Algorithm

Luclidian Algorithm For any integus, a ,b / with azby - GCD (a,b) = GCD (b) a mod b) - GCD (55, 22) = GCD (22, 55 mod Eg: GCD (22, 11 ) 1 11 22 Eg: GCD (18,1. 12) = GCD (1a) 18 mod 12) GCD (13).66 GCD (6, 12 modb) GCD (6,0) 96 Extended Enclidean Algorithm For any given integers a and b, the extended enclidean algorithman not only calculate the GCD 'd' also funds 2 additional integess equation a and y that satisfy The given

axtby=d=gd(a,b) on A c 550 1650 175g it 109,119 17500 :- 1 550 x 1650 1759, 9, 558) 5 109 I 550 104 545 5 log pay pefli 545 28 i ri 9. xi yi -1 1759 I x. ) 0(g_1) O 550 0 (xo) I 1759 mod550 1759/550 3X0 0-3x1 - d R F 109, 3 = = -3 - (sposs) = A al (5/20) 2 550 mod 109 550 109 0-5x1 ej Carbon = 5 (5x-3) =5 5-5 = 16 a on ) s 3 log mod 5 10.91.5 1- 21x-5 - -3 (21x1) St G-74 solubi = 21 106 = -339 of 4 5 mod 4 5/4 -5 (1x106) 16-(1x-ar) 1 = 11b = 355

5 4 mod helps 4/1 4 pagdt gcd( 1759, 550) 1759 X 550 x 355 I = 1759 mod 2.5 12 25 1789 THE ir pafi