Remember that alleles are forms of a gene. So Mendel's 'factors' although referred to as genes are also alleles.
E.g.
Gene: Plant height
Alleles: Tall, short
Mendel found that there were two factors for every characteristic (e.g. height) and that one was dominant over the other. These factors were passed from generation to generation unchanged and govern a specific trait.
He also concluded that there was the Law of Segregation that occurred - this basically says that the factors separate. E.g. If an organism was heterozygous (Tt), then the dominant allele (T) separates from the recessive allele (t)
When they separate, this occurs randomly (do not affect each other as they assort into different gametes) - Law of Independent Assortment.
Because it separates and assorts randomly, this produces a whole range of different combinations of alleles within gametes. Therefore, this produces all different types of gametes in an organism.
Then as a gamete from one organism combines with a gamete from another - a unique combination of alleles is present. This increases variation.
If factors couldn't separate, this wouldn't occur --> no variation.
