I was confused with a question of euclid's division lemma which is stated as follows:Q: Find the HCF of 237and 81 and express it as a linear combination of 81 and 237.please give the solution in at least two ways so that i can choose which is easy for me to understand

 By Euclid 's Division lemma algorithm,

81=75(1) + (6)

237=81(2)+(75)

75=6(12)+(3)

6=3(2)+(0)

HCF  =3

Expressing the HCF as linear combination of 81 and 237 as

HCF =81x +237y

3=75-72

 

3=75-6(12)  

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

 

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)

Thus, x =13 , y =- 38