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