A Bifidus factor is a compound that specifically enhances the growth of bifidobacteria

Bifidobacterium

Bifidobacterium is a genus of Gram-positive, non-motile, often branched anaerobic bacteria. They are ubiquitous, endosymbiotic inhabitants of the gastrointestinal tract, vagina and mouth of mammals and other animals. Bifidobacteria are one of the major genera of bacteria that make up the colon...

 in either a product or in the intestines of humans and/or animals. Several products have been marketed as bifidogenic factors, such as several prebiotics and methyl-N-acetyl D-glucosamine in human milk .
The term is mainly used as a marketing and advertising term.