Difference between revisions of "2021 Fall AMC 12B Problems/Problem 6"
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− | {{duplicate|[[2021 Fall AMC 10B Problems#Problem 8|2021 Fall AMC 10B #8]] and [[2021 Fall AMC | + | {{duplicate|[[2021 Fall AMC 10B Problems#Problem 8|2021 Fall AMC 10B #8]] and [[2021 Fall AMC 12B Problems#Problem 6|2021 Fall AMC 12B #6]]}} |
== Problem == | == Problem == |
Revision as of 00:35, 24 November 2021
- 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
[hide]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