2024 AMC 10A Problems/Problem 5
Revision as of 21:42, 8 November 2024 by Thesmartgreekmathdude (talk | contribs)
- The following problem is from both the 2024 AMC 10A #5 and 2024 AMC 12A #4, so both problems redirect to this page.
Contents
[hide]Problem
What is the least value of such that is a multiple of ?
Solution 1
Note that in the prime factorization. Since is a multiple of and we conclude that is a multiple of Therefore, we have
~MRENTHUSIASM
Note: This is another example where knowing the prime factorization of the year is very useful
Solution 2 (very similar to Solution 1)
Again, note that the prime factorization of 2024 is . We know that for a factorial to contain a prime number , it must be at least . Therefore, we have
~FRANKLIN2013
Video Solution by Daily Dose of Math
~Thesmartgreekmathdude
Video Solution 1 by Power Solve
https://youtu.be/j-37jvqzhrg?si=qwyiAvKLbySyDR7D&t=529
See also
2024 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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 |
2024 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 3 |
Followed by Problem 5 |
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.