Question

If D is the HCF of 40 and 65 find the value of integer X and Y which satisfy the equation D is equals to 40 X + 65 y

Answer 1

40|65|1
-40
____
25|40|1
-25
____
15|25|1
-15
____
10|15|1
-10
____
5|10|2
-10
___
0


so, D=5

65=40(1)+25
40=25(1)+15
25=15(1)+10
15=10(1)+5
10=5(2)+0

5=15-10(1)
=40-25(1)-{25-15(1)}(1)
=40- {65-40}-{65-40-(40-(65-40))}
=40-65+40-65+40+40-65+40
=65(-3)+40(5)

so, x=5, y=(-3)