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What is the greatest prime factor of 6838 ? [#permalink]
1
We have \(6^8 - 3^8\),

but we can see that \(6^8\) is the same as \(2^8*3^8\),

so we now have \(2^8*3^8 - 3^8\)

\(3^8(2^8 - 1)\) here we can use the difference of squares
\(3^8(2^4 - 1)(2^4 + 1)\)

now we are left with \(3^8*15*17\), since 17 is a prime and larger than 3 or 5, the answer is 17.

Answer C.
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What is the greatest prime factor of 6838 ? [#permalink]
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