Question

if d is HCF OF 40 and 65 ,find the value of integers x and y which satisfy d= 40x + 65 y

Answer 1

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Answer 2

Answer:

x = 5 and y = -3

Step-by-step explanation:

65 = 40 × 1 + 25

40 = 25 × 1 + 15

25 = 15 × 1 + 10

15 = 10 × 1 + 5

10 = 5 × 2 + 0

So, HCF(40, 65 ) = 5

⇒ d = 5 = 15 - 10 × 1

5 = 15 - ( 25 - 15 ) × 1

5 = 15 × 2 - 25 × 1

5 = (40 - 25 × 1) × 2 - 25 × 1

5 = 40 × 2 - 25 × 3

5 = 40 × 2 - ( 65 - 40 × 1) × 3

5 = 40 × 5 - 65 × 3

5 = 40 (5) + 65 (-3)

On comparing it with d = 40x + 65y

We get, x = 5 and y = -3