Difference between revisions of "2005 AMC 12B Problems/Problem 21"

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A positive integer $n$ has $60$ divisors and $7n$ has $80$ divisors. What is the greatest integer $k$ such that $7^k$ divides $n$ ?

$\mathrm{(A)}\ {{{0}}} \qquad \mathrm{(B)}\ {{{1}}} \qquad \mathrm{(C)}\ {{{2}}} \qquad \mathrm{(D)}\ {{{3}}} \qquad \mathrm{(E)}\ {{{4}}}$

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 == Problem ==
-{{problem}}
+A positive integer <math>n</math> has <math>60</math> divisors and <math>7n</math> has <math>80</math> divisors.  What is the greatest integer <math>k</math> such that <math>7^k</math> divides <math>n</math>?
+<math>\mathrm{(A)}\ {{{0}}} \qquad \mathrm{(B)}\ {{{1}}} \qquad \mathrm{(C)}\ {{{2}}} \qquad \mathrm{(D)}\ {{{3}}} \qquad \mathrm{(E)}\ {{{4}}}</math>
 == Solution ==
 == See also ==
 * [[2005 AMC 12B Problems]]