16), Find i ICF of 81 and 237 and express it us a linear combination o

1.	16), Find i ICF of 81 and 237 and express it us a linear combination of 81 and 237, le HCF (81,237)-81x+237yfor some x and y
Answer» 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-(8112-7512) 3=75-8112+7512 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

16), Find i ICF of 81 and 237 and express it us a linear combination of 81 and 237, le HCF (81,237)-81x+237yfor some x and y

Answer»

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