Question

if d is the H.C.F of 45 and 27, find x and y satisfying d= 27x +45y.

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

Therefore, HCF = 9

9 = 27 – (18 x 1)
= 27 – [45 – (27 x 1)] x 1 [since 18 = 45 – (27 x 1)]
= 27 – [45 x 1 – 27 x 1 x 1]
= 27 – (45 x 1) + (27 x 1)
= 27 + (27 x 1) – (45 x 1)
= 27{1 + 1} – (45 x 1)
= (27 x 2) – (45 x 1)

HCF of 45 and 27 in the form of 27x + 45 is (27 x 2) + (45 x -1).

Hence, the values of x and y are 2 and -1.

x = 2
y = -1