The numbers are :- 45 and 27 Lets find their HCF BY Euclid's division Lemma :- a = bq + r 45 = 27 x 1 + 18 27 = 18 x 1 + 9 18 = 9 x 2 + 0 HCF = d = 9 Given:- d = 27x+45y 9 = 27x + 45y 9 = 27 - 18 x 1 18 = 45 - 27 x 1 Therefore , 9 = 27 - [ 45 x 27 x 1 ] x 1 = 27 x 2 - 45 9 = 27 x 2 + 45 x [ -1 ] x = 2 y = -1

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