You have supplied:

648581^2 = 6 (mod 2288233)

&

[(880525)(2057202)]^2 = (2)(3) (mod 2288233)

Thus

GCD((880525)(2057202) - 648581 , 2288233) = 1871

This is why:

with the condition that x & yare NOT congruentmodulo n:

subtract

&

Either (x+y) divides n

or (x-y) divides n