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