2017 AMC 8 Problems/Problem 19
Revision as of 21:57, 4 July 2024 by Geometrymystery (talk | contribs) (→Video Solution (CREATIVE THINKING + ANALYSIS!!!))
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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?
Video Solution (Omega Learn)
https://www.youtube.com/watch?v=HISL2-N5NVg&t=817s
~ GeometryMystery