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CBSE Class 10 Answered

if d is the HCF of 45 and 27 find x and y satisfying d=27x+45y?

Asked by bhavikabhatia1125 | 29 May, 2021, 04:12: PM
Expert Answer

HCF of 45 and 27 can be calculated as follows.
45 = 27 x 1 + 18
27 = 18 x 1 + 9
18 = 9 x 2 + 0
 
So, HCF (45, 27) = 9
 
d = 9 = 27x + 45y
 
From above steps, we have:
9 = 27 - 18 x 1
   = 27 - (45 - 27 x 1) x 1
   = 27 x 2 + 45 (-1)

Comparing this with given relation, we get
x = 2 and y = -1

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