Difference between revisions of "2006 SMT/General Problems/Problem 12"
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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 <math>\sqrt{899} \approx 30</math>, we see that 899 is divisible by 29. | 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 is divisible by 29. | ||
Latest revision as of 17:06, 14 January 2020
Solution
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 
, we see that 899 is divisible by 29.
![\[8091=9\cdot899=3^2\cdot29\cdot31\]](http://latex.artofproblemsolving.com/1/a/b/1ab1413671e7662234253952d5e02483afdaa841.png)
Therefore, the largest prime divisor of 8091 is 
