Question

prove

gcd(x , y) = gcd(x, x-y)

Answer 1

this is same as euclid algorithm i dont understand their steps,
i mean i knw using euclod algorithm but i dont understand whats happening between step1 and step2

Answer 2

step1 : 225=135*1+110
step2 : 135=110*1+25
step3 : 110=25*4+10
step4 : 25=10*2+5
step5 : 10=52+0

so, the HCF of 135 and225 is 5.

Answer 3

like why we say the gcd of remainder and small number will give the gcf. that part confuses :S

Answer 4

gcd=a
ka=x
pa=y
(k-p)a=x-y
So\[\gcd(x , y) \ge \gcd(x, x-y)\]Not proved its equality, though