Most of the constructions in the theory of combinatorial geometries take place in the category of pregeometries and strong maps. In this present paper, we study these constructions and the structure of pregeometries by factoring strong maps into elementary maps, after the work of Dowling and Kelly. Using the modular cuts of the factorization to determine certain single-element extensions, we associate each factorization Φ to a unique labeled pregeometry, called the major of Φ. Every major of a factorization of a strong map f:H→G has H and G as distinguished minors: H as a subgeometry; G as a contraction.A partial order is defined on the set of all factorizations of f,
