Question

find hcf of 81 and 237 and express it as a linear combination of 81 and 237 I.e.,hcf(81,237)=81x+237y for some x and y

Answer 1

237=81*2+75..........(1) 81=75*1+6.........(2) 75=6*12+3..........(3) 6=3*2+0.........(4) so the HCF of 81 and 237 will be 3. now to expresss it as a linear combination of 81 and 237 . from(3)we have , 3=75-6*12 =>3=75-(81-75*1)*12 =>3=13*75-12*81 =>3=13*(237-81*2)-12*81 =>3=13*237-26*81-12*81 =>3=13*237-38*81 =>3=237x+81y, where x=130 and y=-38

Answer 2

here is your answer...