Question

if d is the hcf of 45 and 27 find x and y satisfying d=27x+45y.

Answer 1

HCF of 45 and 27 can be calculated as follows.
45 = 27 × 1 + 18
27 = 18 × 1 + 9
18 = 9 × 2 + 0

So, HCF (45, 27) = 9

d = 9 = 27x + 45y

From above steps, we have:
9 = 27 - 18 × 1
= 27 - (45 - 27 × 1) × 1
= 27 × 2 + 45 (-1)
Comparing this with given relation, we get,
x = 2 and y = -1