An example of a local ring of $V$ at $p$ not ufd

Question

Let be $O_{V,p}$ the local ring of an irreducible variety $V$ at point $p$, I would like to know an example where $O_{V,p}$ is not UFD.

Answer 1

Take the zero locus in the plane of $y^2 = x^3$. At the origin there are two factorizations of $y^2$.