Find HCF of 81 and 237 and express it in linear combination of 81 and

1.	Find HCF of 81 and 237 and express it in linear combination of 81 and 237
Answer» Since, 237 > 81On applying Euclid’s division algorithm, we get237 = 81 × 2 + 75 ...(i)81 = 75 × 1 + 6 ...(ii)75 = 6 × 12 + 3 ...(iii)6 = 3 × 2 + 0 ...(iv)Hence, and HCF (81, 237) = 3. 1 Write 3 in the form of 81x + 237y, move backwards3 = 75 – 6 × 12 [From (iii)]= 75 – (81 – 75 × 1) × 12 [Replace 6 from (ii)]= 75 – (81 × 12 – 75 × 1 × 12)= 75 – 81 × 12 + 75 × 12= 75 + 75 × 12 – 81 × 12= 75 ( 1 + 12) – 81 × 12= 75 × 13 – 81 × 12= 13(237 – 81 × 2) – 81 × 12 [Replace 75 from (i)]= 13 × 237 – 81 × 2 × 13 – 81 × 12= 237 × 13 – 81 (26 + 12)= 237 × 13 – 81 × 38= 81 × (– 38) + 237 × (13)= 81x + 237yHence, x = – 38 and y = 13

Discussion