The question of expressing a natural number as sum of two squares in one or two different ways has been of significant importance in mathematics. This question has affirmatively been answered by several prominent mathematicians like Euler, Lagrange, Gauss, Dedekind and many more. In this paper, we will provide nice and elementary techniques by which we can determine the numbers which are expressible as sum of two squares in one or two different ways using the concept of factorization of a number.