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What is the greatest prime factor of the sum of the arithmetic sequence \(1 + 2 + 3 + \cdots + 80\)?

 May 12, 2024
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The sum of an arithmetic series is the number of terms in the series times the average of the first and last term. In this case, the number of terms is 80 and the average of the first and last term is (1+80)/2=40.5. Therefore, the sum of the series is 80⋅40.5=3240.

 

We can now factor 3240. We see that 3240=2⋅2⋅2⋅2⋅3⋅5⋅7. The greatest prime factor is 7​.

 May 13, 2024

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