A hyperplane arrangement A over a finite-dimensional vector space V is a collection of affine hyperplanes. The combinatorial structure of A is captured by its intersection poset L(A), which records the intersections of these hyperplanes. The characteristic polynomial χ(A,t) of A is the most important invariant, with deep connections to combinatorial, algebraic and topological properties of A. In this talk, we will introduce an ideal decomposition of L(A) that enables the factorization of χ(A,t) into the product of characteristic polynomials of lower ideals of L(A).