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Math Help - prime numbers

  1. #1
    Senior Member sfspitfire23's Avatar
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    prime numbers

    What is the greatest prime factor of 3^100-3^97?

    My method:

    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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  2. #2
    MHF Contributor
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    Quote Originally Posted by sfspitfire23 View Post
    What is the greatest prime factor of 3^100-3^97?

    My method:

    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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