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2005 AMC 12B Question 21

AMC12 · 2005 AMC 12B

Question 21

A positive integer $n$ has $60$ divisors and $7n$ has $80$ divisors. What is the greatest integer $k$ such that $7^k$ divides $n?$
  1. $0$
  2. $1$
  3. $2$
  4. $3$
  5. $4$