If d is the Highest Common Factor of 32 and 60, find x and y satisfyin

1.	If d is the Highest Common Factor of 32 and 60, find x and y satisfying d = 32x + 60y.
Answer» Applying Euclid’s divison lemma to 32 and 60, we get 60 = 32 x 1 + 28 … (i) The remainder is 28 ≠ 0. Again applying division lemma 32 = 28 x 1 + 4 … (ii) The remainder 4 ≠ 0. Again applying division lemma 28 = 4 x 7 + 0 … (iii) The remainder zero. ∴ H.C.F. of 32 and 60 is 4. From (ii), we get 32 = 28 x 1 + 4 ⇒ 4 = 32 – 28 x 1 ⇒ 4 = 32 – (60 – 32 x 1) x 1 ⇒ 4 = 32 – 60 + 32 ⇒ 4 = 32 x 2 + (-1) x 60 ∴ x = 2 and y = -1

If d is the Highest Common Factor of 32 and 60, find x and y satisfying d = 32x + 60y.

Answer»

Applying Euclid’s divison lemma to 32 and 60, we get

60 = 32 x 1 + 28 … (i)

The remainder is 28 ≠ 0.

Again applying division lemma

32 = 28 x 1 + 4 … (ii)

The remainder 4 ≠ 0.

Again applying division lemma

28 = 4 x 7 + 0 … (iii)

The remainder zero.

∴ H.C.F. of 32 and 60 is 4.

From (ii), we get

32 = 28 x 1 + 4

⇒ 4 = 32 – 28 x 1

⇒ 4 = 32 – (60 – 32 x 1) x 1

⇒ 4 = 32 – 60 + 32

⇒ 4 = 32 x 2 + (-1) x 60

∴ x = 2 and y = -1