Final answer:
The process of a cell increasing its number by mitotic division is called mitosis, where the nucleus divides into two genetically identical nuclei, followed by cytokinesis.
Step-by-step explanation:
When a cell undergoes a process of increasing cell numbers by mitotic division, it is referred to as mitosis. This process includes a series of phases: prophase, prometaphase, metaphase, anaphase, and telophase, which result in the division of the cell's nucleus. Telophase is followed by cytokinesis, where the cytoplasm divides to generate two genetically identical daughter cells. This is a form of asexual reproduction and is distinct from meiosis, which is the division process for sex cells or gametes.