Question

Find the HCF of 81 and 273 and express it as a linear combination of 81 and 273

Answer 1

= 273 = 81*3 + 30

= 81 = 30*2 + 21

= 30 = 21*1 + 9

= 21 = 9*2 + 3

= 9 = 3*3 + 0

Hence 3 is HCF of 81 and 273.

Fr linear combination :

=) 3 = 21-9(2)

=) 3 = 21- (30-21)2

=) 3 = 21 + 21(2) - 30(2)

=) 3 = 21(3) - 30(2)

=) 3 = {81-30(2)} 3 - 30(2)

=) 3 = 81(3) - 30(8)

=) 3 = 81(3) - {273-81(3)}8

=) 3 = 81(3) - 273(8) + 81(24)

Hence 3 = 81(27) +273(-8)..

Hope it helps u