2021 Fall AMC 10B Problems/Problem 8
Revision as of 21:16, 22 November 2021 by Kingofpineapplz (talk | contribs) (Created page with "==Problem 8== The largest prime factor of <math>16384</math> is <math>2</math>, because <math>16384 = 2^{14}</math>. What is the sum of the digits of the largest prime factor...")
Problem 8
The largest prime factor of 
is 
, because 
. What is the sum of the digits of the largest prime factor of 
?
Solution 1
We have
![\[16383=16384-1=2^{14}-1=(2^7+1)(2^7-1)=129\cdot127=3\cdot43\cdot127\]](http://latex.artofproblemsolving.com/5/f/c/5fcc9d3a1df14467ddf9d38ee8ae114cf1a836f7.png)
Since 
is prime, our answer is 
.
~kingofpineapplz
