2021 Fall AMC 12B Problems/Problem 6
Revision as of 17:36, 24 November 2021 by Ehuang0531 (talk | contribs) (all 3 solutions are the same)
- The following problem is from both the 2021 Fall AMC 10B #8 and 2021 Fall AMC 12B #6, so both problems redirect to this page.
Problem
The largest prime factor of 
is 
because 
. What is the sum of the digits of the greatest prime number that is a divisor of 
?
Solution 1
We want to find the largest prime factor of
![\[16383=16384-1=2^{14}-1=(2^7+1)(2^7-1)=129\cdot127=3\cdot43\cdot127.\]](http://latex.artofproblemsolving.com/3/9/0/39020c045c8422c0f4260c2d523120b5d783d848.png)
Since 
is prime, our answer is 
.
~NH14, kingofpineapplz, and Arcticturn
Video Solution by Interstigation
https://youtu.be/p9_RH4s-kBA?t=1121
See Also
| 2021 Fall AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
| 2021 Fall AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 5 |
Followed by Problem 7 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
