Question

find hcf of 63 and 81 and express it in forum of d = 63x + 81 y

Answer 1

Hey there !

Solution:

Using Euclid's Division Lemma, we get,

=> 81 = 63 × 1 + 18

=> 63 = 18 × 3 + 9

=> 18 = 9 × 1 + 0

=> HCF of 63 and 81 = 9

=> 9 = 63 - 54

=> 9 = 63 - ( 18 × 3 )

=> 9 = 63 - [ ( 81 - 63 ) × 3 ]     [ ∵ 81 - 63 = 18 ]

=> 9 = 63 - [ 81 ( 3 ) - 63 ( 3 ) ]

=> 9 = 63 - 81 [ 3 ] + 63 ( 3 )

=> 9 = 63 ( 4 ) - 81 ( 3 )

=. 9 = 63 ( 4 ) + 81 ( - 3 )

Hence 9 = 63 x + 81 y can be written as 63 ( 4 ) + 81 ( - 3 )

Hence x = 4 and y = -3.

Hope my answer helped !