Question

If d is the HCF of 30 and 72, find the values of x and y,satisfying d=30x+72y, find x and y

Answer 1

Using Euclid’s algorithm, the HCF (30, 72)72 = 30 × 2 + 12      30 = 12 × 2 + 612 = 6 × 2 + 0HCF (30,72) = 66=30-12×26=30-(72-30×2)26=30-2×72+30×46=30×5+72×-2\ x = 5, y = -2Also 6 = 30 ×5 + 72 (-2) + 30 × 72 – 30 × 72Solve it, to getx = 77, y = -32Hence, x and y are not unique