The ring of integer-valued polynomials over a given subset S ℤ (or Int(S,ℤ)) is defined as the set in ℚ[x] which maps to ℤ. In factorization theory, it crucial check irreducibility polynomial. this article, we make Bhargava factorials our main tool polynomial f∈Int(S,ℤ)). We also generalize results arbitrary subsets Dedekind domain.