2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113002We give a relatively easy proof of the Erd\H os-Kac theorem via computing moments. We show how this proof extends naturally in a sieve theory context, and how it leads to several related results in the literature.12 pages; expository article, to appear in the Montreal NATO school on equidistributionNumber TheoryProbabilitytext