Difference between revisions of "2017 AMC 8 Problems/Problem 19"
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− | Note: Can you say what formula this uses? most AMC 8 test takers won't know it. Also, can someone unvandalize this page? | + | Note: Can you say what formula this uses? most AMC 8 test takers won't know it. Also, can someone unvandalize this page at the top? |
==Video Solution (Omega Learn)== | ==Video Solution (Omega Learn)== |
Revision as of 13:47, 16 August 2024
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Problem
For any positive integer , the notation M! denotes the product of the integers 1 through M. What is the largest integer for which is a factor of the sum ?
Solution 1
Factoring out , we have , which is . Next, has factors of . The is because of all the multiples of .The is because of all the multiples of . Now, has factors of , so there are a total of factors of .
~CHECKMATE2021
Note: Can you say what formula this uses? most AMC 8 test takers won't know it. Also, can someone unvandalize this page at the top?
Video Solution (Omega Learn)
https://www.youtube.com/watch?v=HISL2-N5NVg&t=817s
~ GeometryMystery
See Also
2017 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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 AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.