Question

find the H.C.F. of 81 and 237 and express it as a linear combination of 81 and 237.. plz answer...i wil giv thumbs up..plz!!

Answer 1

3 = 75 - (81 - 75 x 1) x 12...............(1)
Now, apply multiplication and distribution rule i.e. a(b+c)=ab+bc
? (1) becomes
=> 3 = 75 - (81 x 12 - 75 x 12)
Now open the bracket...so sign changes from -75 to +75
=> 3 = 75 - 81 x 12 + 75 x 12
=> 3 = 75 + 75 x 12 - 81 x 12
=> 3 = 75 (1 + 12) - 81 x 12
=> 3 = 75 x 13 - 81 x 12...............(2)
75 = 237 – 81 x 2 ? from your step 1..............(3)
Substitue (3) in (2)
=> 3 = (237 - 81 x 2) x 13 - 81 x 12
Apply again multiplication and distribution rule,
=> 3 = 237 x 13 - 81 x 2 x 13 - 81 x 12
=> 3 = 237 x 13 - 81 x 26 - 81 x 12
=> 3 = 237 x 13 - 81 (26 + 12)
=> 3 = 237 x 13 - 81 x 38....................(4)
HCF(237,81) = 3 = 237 x 13 + 81 x (-38) ? from (4)...........(5)
Solve (4) and (5) the answer will be same i.e. 3
? 3 = 237x + 81y where x = 13 and y = (-38)