  There is a well-known analogy between integers and polynomials over $F_q$,
and a vast literature on analytic number theory for polynomials. From a
geometric point of view, polynomials are equivalent to effective 0-cycles on
the affine line. This leads one to ask: Can the analogy between integers and
polynomials be extended to 0-cycles on more general varieties? In this paper we
study prime factorization of effective 0-cycles on an arbitrary connected
variety $V$ over $F_q$, emphasizing the analogy between integers and 0-cycles.
For example, inspired by the works of Granville and Rhoades, we prove that the
prime factors of 0-cycles are typically Poisson distributed.
