Question

find the had of 81 and 237 and express it as a linear combination of 81 and 237.

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.now to xpress it as a linear combination of 81 and 237.from (3)we have=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,y=38.