Question

find hcf of 81 and 237 and express it as linear combination of 81x+237y

Answer 1

hello there !!!
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.