Difference between revisions of "2017 AMC 8 Problems/Problem 19"
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Revision as of 20:38, 10 June 2024
Problem
For any positive integer , the notation
denotes the product of the integers
through
. 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
Video Solution (CREATIVE THINKING + ANALYSIS!!!)
https:/90ijn bidxrfgv