"Factor" was Mendel's word for a unit of heredity, which in the modern era has come to be called gene. However, whereas "gene" is a word with several different meanings, "factor" has a precisely defined meaning as a single unit of heredity that corresponds to only two alleles.
The inheritance of Mendel's factors is defined by his two laws: the law of segregation and the law of independent assortment. Although the law of segregation is pretty solid, the law of independent assortment does not hold in general due to recombination during meiosis.
