Cell multiplication is part of a process called the cell cycle. Cells need to constantly replace themselves with fresh copies. A large part of the cell cycle is called Mitosis. Sometimes there is a mutation and malfunction and cells multiple out of control - this is what we call cancer.
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Cell growth and multiplication is a continual process, and most often carefully controlled. The whole process is called mitosis. The cell prepares to split by organizing everything in side the cell. That is the Prophase. When the chromosomes are ready to separate it is the Metaphase. When the chromatids separate, it is called the Anaphase. And lastly, the split itself is called the Telophase. You can find more information here: http://info.cancerresearchuk.org/youthandschools/latestfromthelab/howcellswork/howcellsmultiply/index.htm