Difference between revisions of "2021 Fall AMC 10B Problems/Problem 8"
(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...") |
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We have | We have | ||
| − | <cmath>16383=16384-1=2^{14}-1=(2^7+1)(2^7-1)=129\cdot127=3\cdot43\cdot127</cmath> | + | <cmath>16383=16384-1=2^{14}-1=(2^7+1)(2^7-1)=129\cdot127=3\cdot43\cdot127.</cmath> |
Since <math>127</math> is prime, our answer is <math>\boxed{\textbf{(C) }10}</math>. | Since <math>127</math> is prime, our answer is <math>\boxed{\textbf{(C) }10}</math>. | ||
~kingofpineapplz | ~kingofpineapplz | ||
Revision as of 22:17, 22 November 2021
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/3/9/0/39020c045c8422c0f4260c2d523120b5d783d848.png)
Since 
is prime, our answer is 
.
~kingofpineapplz
