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2006 SMT/General Problems/Problem 12

Revision as of 17:01, 14 January 2020 by Dividend (talk | contribs) (Created page with "Noticing that the sum of the digits of 8091 is 18, we can divide 8091 by 9, yielding 899. Testing all prime numbers up to <math>\sqrt{899} \approx 30</math>, we see that 899 i...")
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Noticing that the sum of the digits of 8091 is 18, we can divide 8091 by 9, yielding 899. Testing all prime numbers up to $\sqrt{899} \approx 30$, we see that 899 is divisible by 29.

\[8091=9\cdot899=3^2\cdot29\cdot31\]

Therefore, the largest prime divisor of 8091 is $\boxed{31}$

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