Grade 1010 grade maths
If hcf of 81 and 237 can be expressed as 81x + 237y then find the value of 3x+2y
1 Answer
Arun
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
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