Question

If d is the hcf of 45 and 27 , find the value of x and y satisfying d = 27x +45y give solutions step by step

Answer 1

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