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Difference between revisions of "2010 AMC 12B Problems/Problem 25"

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== Problem 25 ==
 
For every integer <math>n\ge2</math>, let <math>\text{pow}(n)</math> be the largest power of the largest prime tha divides <math>n</math>. For example <math>\text{pow}(144)=\text{pow}(2^4\cdot3^2)=3^2</math>. What is the largest integer <math>m</math> such that <math>2010^m</math> divides
 
For every integer <math>n\ge2</math>, let <math>\text{pow}(n)</math> be the largest power of the largest prime tha divides <math>n</math>. For example <math>\text{pow}(144)=\text{pow}(2^4\cdot3^2)=3^2</math>. What is the largest integer <math>m</math> such that <math>2010^m</math> divides
  

Revision as of 16:32, 12 July 2010

Problem 25

For every integer $n\ge2$, let $\text{pow}(n)$ be the largest power of the largest prime tha divides $n$. For example $\text{pow}(144)=\text{pow}(2^4\cdot3^2)=3^2$. What is the largest integer $m$ such that $2010^m$ divides

$\prod_{n=2}^{5300}\text{pow}(n)$?


$\textbf{(A)}\ 74 \qquad \textbf{(B)}\ 75 \qquad \textbf{(C)}\ 76 \qquad \textbf{(D)}\ 77 \qquad \textbf{(E)}\ 78$

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