CGAL 4.14.3  Algebraic Foundations

A model of UniqueFactorizationDomain
is an IntegralDomain
with the additional property that the ring it represents is a unique factorization domain (a.k.a. UFD or factorial ring), meaning that every nonzero nonunit element has a factorization into irreducible elements that is unique up to order and up to multiplication by invertible elements (units). (An irreducible element is a nonunit ring element that cannot be factored further into two nonunit elements. In a UFD, the irreducible elements are precisely the prime elements.)
In a UFD, any two elements, not both zero, possess a greatest common divisor (gcd).
Moreover, CGAL::Algebraic_structure_traits< UniqueFactorizationDomain >
is a model of AlgebraicStructureTraits
providing: