Question

find the HCF of 240 and 1024 and express it as a linear combination of 240 and 1024.

Answer 1

From Step 1;

75 = 237 – 81 × 2

Thus, from Step 6;

3 = (237 – 81 × 2) × 13 – 81× 12

⇒ 3 = (237 × 13 – 81 × 26) – 81× 12

⇒ 3 = 237 × 13 – 81 × 38

⇒ H.C.F. of 237 and 81 = 237 × 13 + 81 × (–38)

∴HCF, 3 can be expressed as linear combination of 81 and 237 as 3 = 81x + 237y, where x and y are not unique.