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Quick Answer.  Noble gases are unreactive because their outer electron shells are full and therefore in their most stable state. Normally, elements react with one another because they have incomplete electron shells. They lose, gain or share electrons in order to gain a more stable electron configuration.
For the first six periods of the periodic table, the noble gases are exactly the members of group 18 of the periodic table. It is possible that due to relativistic effects, the group 14 element flerovium exhibits some noble-gas-like properties, instead of the group 18 element ununoctium. Noble gases are typically highly unreactive except when under particular extreme conditions.