Question

If d is HCF of 40 and 65,find the value of integer x and you wch satisfy d=40x+65y

Answer 1

[ How to find the HCF is in the attachment ]

By Euclid's Division lemma :-

a = bq + r

65 = 40 × 1 + 25

40 = 25 × 1 + 15

25 = 15 × 1 + 10

15 = 10 × 1 + 5

10 = 5 × 2 + 0

So, the HCF = 5

And HCF is denoted as d

5 = 15 - 10 × 1

5 = 15 - ( 25 - 15 × 1 ) × 1

5 = 15 - 25 × 1 + 15 × 1

5 = 15 + 15 × 1 - 25 × 1

5 = 15 ( 1 + 1 ) - 25 × 1

5 = 15 × 2 - 25 × 1

5 = ( 40 - 25 × 1 ) × 2 - 25 × 1

5 = 40 × 2 - 25 × 2 - 25 × 1

5 = 40 × 2 - 25 ( 2 + 1 )

5 = 40 × 2 - 25 × 3

5 = 40 × 2 - ( 65 - 40 × 1 ) × 3

5 = 40 × 2 - 65 × 3 + 40 × 3

5 = 40 ( 2 + 3 ) - 65 × 3

5 = 40 × 5 - 65 × 3

Comparing between d = 40x + 65y
and 5 = 40 × 5 - 65 × 3

we get ,

x = 5

y = - 3

Answer 2

HCF = 5

x = 5
y = -3