Why is AUM chanted 21 times?

AUM chanting is a purifying and balancing kriya. The longer it is done for the more pronounced the effects will be. It is chanted 21 times to purify different aspects and dimensions of the human system. This is symbolic of course. The cleansing happens at a deeper cellular and Pranic level. 

• Five AUMs are chanted for the organs of action: vocal chords, hands, feet, elimination organs (represented by the anus), and
  generative organs.
• Five AUMs are for the organs of perception: eye, ear, nose, tongue, and skin, which correspond to sight, hearing, smell,
  taste, and touch.
• Five AUMs are for the five vital airs of the body. English doesn't seem to have names for these vital airs, so we list them with their Sanskrit names. They are: prana (located in lungs), apana (flatus, which moves downward through the rectum), vyana (diffused throughout the whole body), samana (navel; essential to digestion), and udana (rises through throat to head).
• Five AUMs are for the five sheaths or encasings of the body: the material sheath, the sheath of vital air, the mental-emotional sheath, the sheath of intellect, and the sheath of bliss.
• The last AUM is for the person itself --and the person's self-realisation.