Question

If D is the HCF of 56 and 72 find X and Y satisfying d = 56 X + 72 Y show that x and y are not unique???

Answer 1

To show these are not unique, multiply whole eq by any natural no.

Answer 2

Step-by-step explanation:

Using Euclid's algorithm, the HCF(56,72)

72 = 56 * 1 + 16    ---- (i)

56 = 16 * 3 + 8     ----- (ii)

16 = 8 * 2 + 0       ------ (iii)

Since, Remainder is 0. HCF of 56 and 72 is 8.

From (ii), we get

8 = 56 * 16 * 3

8 = 56 - (72 - 56 * 1) * 3

8 = 56 - 3 * 72 + 56 * 3

8 = 56 * 4 + (-3) * 72

On comparing with 56x + 72y, we get

x = 4, y = -3.

Now,

8 = 56 * 4 + (-3) * 72

8 = 56 * 4 + (-3) * 72 - 56 * 72 + 56 * 72

8 = 56 * 4 - 56 * 72 + (-3) * 72 + 56 * 72

8 = 56 * (4 - 72) [(-3) + 56] * 72

8 = 56 * (-68) + 53 * (72)

On comparing we get, x = -68 , y = 53.

Hence, x and y are not unique.

Hope it helps!