Question

If ‘d ‘ is the H.C.F of 963 & 657, Find the value of x & y satisfying d = 963x + 657y.

Answer 1

answer : x = -15 and y = 22

d is the HCF of 963 and 657 .

prime factors of 963 = 3 × 3 × 107

prime factors of 657 = 3 × 3 × 73

HCF of 963 and 657 = highest common factors of 963 and 657 = 3 × 3

⇒d = 9

given, d = 963x + 657y

⇒9 = 963x + 657y

⇒1 = 107x + 73y.......(1)

putting x = -15 and y = 22

⇒1 = 107 × (-15) + 73 × 22

hence x = -15 and y = 22

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Answer 2

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x = -15

y = 22