In this talk, we prove the unique factorization property of Schur functions. This fundamental property of Schur functions was first observed and proved by C. S. Rajan in 2004. I give a different proof of this beautiful fact which I jointly obtained with my adviser S. Viswanath. I begin my talk with introducing the Schur functions and their connections with representation theory of general linear groups. Basic knowledge of elementary algebra will be assumed like group theory and linear algebra. If time permits, I will tell you about the possible generalizations of this result.