Cyanobacteria and bacteria do not reproduce by mitosis because they only contain one chromosome.
Mitosis involves the equational division of vegetative cells.
During mitosis, sister chromatids separate and migrate to the opposite poles with the same cytoplasm. The cytoplasm eventually divides by cytokinesis to produce two independent daughter cells that are not only genetically similar to each other, but also to their parent.
Cyanobacteria and bacteria have just a single chromosome in their genome. Thus, it is impossible for this chromosome to separate, migrate to the opposite poles. and produce 2 daughter cells.
Both organisms are living and reproduce by other means such as binary fission, conjugation, etc.
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