If p is the prodcut 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
A) 10
B) 12
C) 14
D) 16
E) 18
So, the question is asking for the greatest number of 3s in p.jnbimmer wrote:If p is the prodcut 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
The easiest way to do it is to write out the multiples of 3:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30...that's 10
Because 9 is 3^2, as multiples of 9, each of 9 and 18 have one extra 3. And 27 is 3^3, so there are two extra 3s there. That's a total of 14 3s. Choice C.
