1. Good post? |

## quicker method??

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

2. Good post? |
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 ?

3. Good post? |
The question is asking how many factors of 3 are in 30!

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

4. Good post? |
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 ?

5. Good post? |
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.

6. Good post? |
C for me too
Following method can be used to calculate this

30/3 = 10
10/3 = 3
3/1 = 1

7. Good post? |
Originally Posted by NishantG
C for me too
Following method can be used to calculate this

30/3 = 10
10/3 = 3
3/1 = 1
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

8. Good post? |
Thanks BoB for the correction in the question otherwise I was just wondering how to approach about it.

There are currently 1 users browsing this thread. (0 members and 1 guests)

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•

SEO by vBSEO ©2010, Crawlability, Inc.