How does a prokaryotic cell divide?

Prokaryotic cells divide through binary fission, a simple and rapid cell division process.  

All prokaryotic cells are unicellular. The genome consists of a single, circular DNA chromosome that is present in the nucleoid, a simple open area in the center of the cell. Because of the relatively simple structure and genomic composition of prokaryotic cells, the cell division process is also highly simplified.  

Replication of the DNA starts in a region close to where the DNA is attached to the plasma membrane, which is about the midpoint of the cell. Once it begins, the replication of the chromosome moves in a bidirectional pattern, with each origin point moving away from the cell wall attachment towards opposite ends of the cell at the same time. This results in the formation of new double strands. 

The chromosomes eventually clear the midpoint of the cell as the cell elongates, marking the beginning of the cytoplasmic separation. FtsZ proteins dispersed throughout the cytoplasm migrate towards the center of the cell and form a ring at the midpoint between the chromosomes. 

The FtsZ ring attracts new membrane and cell wall materials to the site, creating a septum between the newly formed nucleoids. The septum gradually extends from the periphery towards the midpoint of the cell. On completion of the septum, the cell wall pinches into two separate entities, forming two identical daughter cells. The FtsZ proteins are released back into the cytoplasm of the new cells.