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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.
In the noble-gas atoms, the electron shells are completely filled; thus, the elements are almost completely inert. The other nonmetals have nearly filled electron shells, requiring only a few additional electrons to assume the stable, noble-gas configuration. Therefore, in the presence of other atoms, these nonmetallic atoms have pronounced tendencies to attract electrons to themselves (high electronegativities).