2017 AMC 8 Problems/Problem 19: Difference between revisions
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==Problem== | |||
For any positive integer <math>M</math>, the notation M! denotes the product of the integers 1 through | |||
M. What is the largest integer <math>n</math> for which <math>5^n</math> is a factor of the sum <math>98!+99!+100!</math> ? | |||
<math>\textbf{(A) }23 \qquad \textbf{(B) }24 \qquad \textbf{(C) }25 \qquad \textbf{(D) }26 \qquad \textbf{(E) }327</math> | |||
==Solution 1== | ==Solution 1== | ||
Revision as of 20:49, 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 (CREATIVE THINKING + ANALYSIS!!!)
https:/90ijn bidxrfgv
