2021 Fall AMC 12B Problems/Problem 6
- 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.
Contents
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 have
Since
is prime, our answer is
.
~kingofpineapplz
Solution 2
Since is
, we can consider it as
.
is
less than
, so it can be considered as
less than a square. Therefore, it can be expressed as
. Since
is
is
.
is
, and since
is larger, our answer is
.
~Arcticturn
Solution 3
We want to find the largest prime factor of Thus, the largest prime factor is
which has the sum of the digits as
Thus the answer is
~NH14
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.