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 ?	Choose the correct choice from the following options:
A) 10	B) 12	C) 14	D) 16	E) 18
Thus proceeding with the "300 + k" assumption, we get:   P = 30!   Option A: 310   =&gt; 310 = 2 * 5 * 31   =&gt; 31 is a prime and is not present in 30!   Thus 310 is not a factor of P   =&gt; A is Eliminated   Option 12: 312   =&gt; 312 = 2^3 * 3 * 13   Thus 312 is a factor of P   =&gt; 12 is the correct answer !   Option C: 314   =&gt; 314 = 2 * 157   =&gt; 157 is a prime and is not present in 30!   Thus 314 is not a factor of P   =&gt; C is Eliminated   Option D: 316   =&gt; 316 = 2^2 * 79   =&gt; 79 is a prime and is not present in 30!   Thus 316 is not a factor of P   =&gt; D is Eliminated   Option E: 318   =&gt; 310 = 2 * 3 * 53   =&gt; 53 is a prime and is not present in 30!   Thus 318 is not a factor of P   =&gt; E is Eliminated   ANS: 12
<result>B</result>
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 ?