Question

Find hcf of 81 and 237 and express in form 237x+81y

Answer 1

By Euclid's Division Algorithm,

237=81(2)+(75)

81=75(1) + (6)

75=6(12)+(3)

6=3(2)+(0)

Hcf =3

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

3=75-6(12) { From 2nd last step}

3=75-(81-75)(12) {Substituting}

3=75-(81*12-75*12)

3=75-81*12+75*12

3=75(13)-81(12)

3=(237-81*2)(13)-81(12)

3=237(13)-81(38)

3=237(13)+81(-38) {we need an expression in the form 237x + 81y }

Therefore, x =13 , y =- 38