2021 Fall AMC 12B Problems/Problem 6
Revision as of 01:14, 24 November 2021 by Kingofpineapplz (talk | contribs)
- 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