Question

If d is the HCF of 40 and 65 than find x and y if d = 40x + 65y

Answer 1

HCF(40,65)=5

40=5×8
65=5×13

5/2=40×(1/16)=40x
x=1/16

5/2=65×(1/26)=65y
y=1/26

Answer 2

65=40×1+25
40=25×1+15
25=15×1+10
15=10×1+5
10=5×2+0
hence hcf=5
from 4
5=15-10
5=15-(25-15)=15-25+15=2×15-25
5=2×(40-25)-25=2×40-3×25
5=2×40-3×(65-40)=2×40-3×65+3×40
5=5×40+(-3×65) on comparing x=5 and y=-3