CBSE Class 10 Answered
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
Asked by Sanchit Sharma | 30 Apr, 2014, 05:37: PM
Expert Answer
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
Answered by Avinash Soni | 03 May, 2014, 06:22: PM
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