Question

Q find the hcf of 81 and 237 and express it as a linear combination of 81 and237 solution

Answer 1

See... 3 = 75 - 6 x 12 => 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) Hope u got it.