Question

If d is the HCF of 45 and 27, find x,y satisfying d= 27x+ 45y

Answer 1

Answer:

x = -3,y = 2

Step-by-step explanation:

Given :

To find the value of d, such that d = HCF{45,27} and to express d = 27x + 45y for some values  (x,y)∈ Ζ

We know that,

45 = 3 × 3 × 5

and

27 = 3 × 3 × 3

Hence,

HCF{45,27} = 3 × 3 = 9,

We need to find the values of x & y for the equation,

d = 27x + 45y,

By trial & error,

We get,

9 = 27(-3) + 45(2)

⇒ x = -3 , y = 2