If \(p\) is the product of the integers from \(1\) to \(30,\) inclusive, what is the greatest integer \(k\) for which

[Vincen]

If \(p\) is the product of the integers from \(1\) to \(30,\) inclusive, what is the greatest integer \(k\) for which \(3^k\) is a factor of \(p?\)

A. 10
B. 12
C. 14
D. 16
E. 18

Answer: C

Source: Official Guide