AMC 12B 2005 Problem 21

Past Contests AMC 12 AMC 12B - 2005
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1

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

Answer Choices
A. 0
B. 1
C. 2
D. 3
E. 4