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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.
The most characteristic property of the noble gases is their extremely low chemical reactivity as compared to other elements. The noble gases all have a full set of electrons in their outer shells, so they have little tendency to trade electrons with other elements to form compounds.