quicker method??

[raunekk]

If

p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3k is a factor of p?
A. 10
B. 12
C. 14
D. 16

E. 18

[flex_manny]

The question seems a bit weird.
If pis the product of all integers from 1 to 30 that is 30!, then k can be much higher.Of call the given choices I would choose 18. Cause 18 is one of the integers in the product p.

Can you confirm this question ?

[grems]

The question is asking how many factors of 3 are in 30!

30/3 = 10
30/3^2 =3
30/3^3=1

Therefore, the answer is 10+3+1=14

Answer C

[800Bob]

The question is mistyped. It should be:

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 ?

[Fiver]

Subsequent to the correction by BoB.
30/3=10
10/3=3
3/3=1
Therefore 10+3+1=14
Basically we are looking at multiples of 3 hence that many number of 3s (i.e. 10) and other ways in which a 27 can be formed (e.g. 9 *3) etc.

C is my answer.

[NishantG]

C for me too
Following method can be used to calculate this

30/3 = 10
10/3 = 3
3/1 = 1
Answer 10+3+1 = 14

[sandeep_chads]

C for me too
Following method can be used to calculate this

30/3 = 10
10/3 = 3
3/1 = 1
Answer 10+3+1 = 14

For those unaware of this formula it simply comprehends to :

How many factors of 3 in 30! - [3,6,9,,,30] = [30/3] = 10
How many factors of 9 in 30! - [9,18,27] = [30/9] = 3
How many factors of 27 in 30! - [27] = [30/27] = 1

where 30! = 1x2x3x...30

ANs = 10+3+1

[sanjeev_sharma]

Thanks BoB for the correction in the question otherwise I was just wondering how to approach about it.