What is the greatest prime factor of 3^100-3^97? My method: $\displaystyle 3^{100}-3^{97}=3^{97}(3^{3}-1)=3^{97}(26)$. 13 is a factor of 26 and so 13 is the greatest prime factor. Can I deduce that from what I just did?
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Originally Posted by sfspitfire23 What is the greatest prime factor of 3^100-3^97? My method: $\displaystyle 3^{100}-3^{97}=3^{97}(3^{3}-1)=3^{97}(26)$. 13 is a factor of 26 and so 13 is the greatest prime factor. Can I deduce that from what I just did? Yes, 3, 13 and 2 are the prime factors.
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