Question

Find the HCF of 81 and 237 and express it as a linear combination of 81 and 237.​

Answer 1

Answer:

=) By Euclid's Division Algorithm,

237=81(2)+(75).....(1)

81=75(1) + (6).....(2)

75=6(12)+(3).....(3)

6=3(2)+(0)

HCF =3

=)Expressing it in the form of 237x+81y=HCF

3=75-6(12).......from(3)

3=75-(81-75)(12)......from(2)

3=75-(81×12-75×12)

3=75-81×12+75×12

3=75(13)-81(12)

3=(237-81×2)(13)-81(12).....from(1)

3=237(13)-81(38)

3=237(13)+81(-38)

Therefore, x =13 , y =- 38

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