Polynomial ring/K/Common divisor/Definition

Let ${\displaystyle {}P_{1},\ldots ,P_{n}\in K[X]}$ denote polynomials over a field ${\displaystyle {}K}$. We say that a polynomial ${\displaystyle {}T\in K[X]}$ is a common divisor of the given polynomials if ${\displaystyle {}T}$ divides every ${\displaystyle {}P_{i}}$.