Difference between revisions of "2017 AMC 8 Problems/Problem 19"
(→Solution 1) |
(→Video Solution (CREATIVE THINKING + ANALYSIS!!!)) |
||
Line 15: | Line 15: | ||
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? | ||
− | ==Video Solution ( | + | ==Video Solution (Omega Learn)== |
− | https:/ | + | https://www.youtube.com/watch?v=HISL2-N5NVg&t=817s |
+ | |||
+ | ~ GeometryMystery |
Revision as of 21:57, 4 July 2024
wertesryrtutyrudtu
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