Last visit was: 22 Apr 2026, 02:13 It is currently 22 Apr 2026, 02:13
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
Futuristic
User avatar
Joined: 28 Dec 2005
Last visit: 07 May 2009
Posts: 415
Own Kudos:
52
Posts: 415
Kudos: 52
What is the largest power of 55 that can divide 274! Updated on: 15 Sep 2006, 07:02
Originally posted by Futuristic on 15 Sep 2006, 04:28.
Last edited by Futuristic on 15 Sep 2006, 07:02, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
N
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

History

Date
Time
Result
Not Attempted Yet
What is the largest power of 55 that can divide 274! ?



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
yezz
User avatar
Retired Moderator
Joined: 05 Jul 2006
Last visit: 26 Apr 2022
Posts: 830
Own Kudos:
1,686
Given Kudos: 49
Posts: 830
Kudos: 1,686
What is the largest power of 55 that can divide 274! 15 Sep 2006, 06:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The largst power of 55 that devides 274! is that of 11 ...am i right ?

still i cant approach the problem but am i going the right direction or not?
User avatar
haas_mba07
User avatar
Joined: 02 Jun 2006
Last visit: 26 Jun 2008
Posts: 662
Own Kudos:
218
Posts: 662
Kudos: 218
What is the largest power of 55 that can divide 274! 15 Sep 2006, 06:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
hmmm.. I seem to be missing something.

Given

1x2x3.... 274 = 55^k x m

where m is some integer.

As 55 = 11 x 5

The maximum value of k can be the maximum power of 11 (as 11 > 5).

Therefore # of multiples of 11 from 1 to 274
= (264-11)/11 +1 = 24

11 x 22 x 33 x 44... x 264
= 11^24 x 2 x 3 x 4 x .. 24
= 11^24 x 11^2 x K (as there are two more multiples of 11 from 2..24)

=11^26.

This should be 26.. but all options are three digits.

Not sure...

Help futuristic!!! :(
User avatar
Futuristic
User avatar
Joined: 28 Dec 2005
Last visit: 07 May 2009
Posts: 415
Own Kudos:
52
Posts: 415
Kudos: 52
What is the largest power of 55 that can divide 274! 15 Sep 2006, 07:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Sorry guys, I sincerely apologize....got 2 questions mixed up in my sleep. Should not post at 4am in the morning....haas your answer is correct:)
:wall
User avatar
haas_mba07
User avatar
Joined: 02 Jun 2006
Last visit: 26 Jun 2008
Posts: 662
Own Kudos:
218
Posts: 662
Kudos: 218
What is the largest power of 55 that can divide 274! 15 Sep 2006, 07:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thanks for clarifying Futuristic..all of us have done it at one time or another.

Get some sleep though :sleep :sleep :sleep .. :P

Futuristic
Sorry guys, I sincerely apologize....got
2 questions mixed up in my sleep. Should not post at 4am in the morning....haas your answer is correct:)
:wall
Show more
User avatar
trivikram
User avatar
Joined: 28 Mar 2006
Last visit: 25 May 2018
Posts: 669
Own Kudos:
65
Posts: 669
Kudos: 65
What is the largest power of 55 that can divide 274! 15 Sep 2006, 21:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
haas_mba07
hmmm.. I seem to be missing something.

Given

1x2x3.... 274 = 55^k x m

where m is some integer.

As 55 = 11 x 5

The maximum value of k can be the maximum power of 11 (as 11 > 5).

Therefore # of multiples of 11 from 1 to 274
= (264-11)/11 +1 = 24

11 x 22 x 33 x 44... x 264
= 11^24 x 2 x 3 x 4 x .. 24
= 11^24 x 11^2 x K (as there are two more multiples of 11 from 2..24)

=11^26.

This should be 26.. but all options are three digits.

Not sure...

Help futuristic!!! :(
Show more


As unrelenting as you can be...Just awesome
User avatar
cicerone
User avatar
Joined: 28 Aug 2006
Last visit: 10 May 2019
Posts: 163
Own Kudos:
316
 [1]
Posts: 163
Kudos: 316
 [1]
What is the largest power of 55 that can divide 274! Updated on: 25 Sep 2008, 01:09
Originally posted by cicerone on 16 Sep 2006, 01:45.
Last edited by cicerone on 25 Sep 2008, 01:09, edited 1 time in total.
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Folks, I'll tell u how to calculate highest power of a number in any factorial.

Taking the above example 55 = 11x5
Since the highes power of 11 in any factorial will be less than the highest power of 5 it is just enough to calculate highest power of 11 in 274!

I think someone has already suggested a method to calculate highest power.

Let's look at one more way (The logic is same as mentioned earlier)

274/11 = 24 (don't worry about the remainder)
24/11 = 2
Add up now 24+2 = 26 will be the highest power of 11 in 274!

Let's look at one more example.
Highest power of 5 in 350!
350/5 = 70
70/5 = 14
14/5 = 2
So 70+14+2 = 86 is the highes power of 5 in 350!.
I guess the explanation is lucid
User avatar
haas_mba07
User avatar
Joined: 02 Jun 2006
Last visit: 26 Jun 2008
Posts: 662
Own Kudos:
218
Posts: 662
Kudos: 218
What is the largest power of 55 that can divide 274! 16 Sep 2006, 07:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thanks Cicerone... thats a great and quick way to solve a problem like this... this should help shorten the time to calculate.

Can you post a link relevant to this calculation?

Thanks/

cicerone
Folks, I'll tell u how to calculate highest power of a number in any factorial.

Taking the above example 55 = 11x5
Since the highes power of 11 in any factorial will be less than the highest power of 5 it is just enough to calculate highest power of 11 in 274!

I think someone has already suggested a method to calculate highest power.

Let's look at one more way (The logic is same as mentioned earlier)

274/11 = 24 (don't worry about the remainder)
24/11 = 2
Add up now 24+2 = 26 will be the highest power of 11 in 274!

Let's look at one more example.
Highest power of 5 in 350!
350/5 = 70
70/5 = 14
14/5 = 2
So 70+14+2 = 86 is the highes power of 5 in 350!.
I guess the explanation is lucid
Show more
User avatar
Futuristic
User avatar
Joined: 28 Dec 2005
Last visit: 07 May 2009
Posts: 415
Own Kudos:
52
Posts: 415
Kudos: 52
What is the largest power of 55 that can divide 274! 16 Sep 2006, 12:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The method mentioned here is what I learnt as well...check out 4gmat.com number properties book.
User avatar
heman
User avatar
Joined: 20 Mar 2006
Last visit: 12 Dec 2006
Posts: 104
Own Kudos:
10
Posts: 104
Kudos: 10
What is the largest power of 55 that can divide 274! Updated on: 16 Sep 2006, 19:37
Originally posted by heman on 16 Sep 2006, 19:15.
Last edited by heman on 16 Sep 2006, 19:37, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Futuristic
What is the largest power of 55 that can divide 274! ?
Show more


55= 11*5

#multiples of 11 in 274! = 11,22,33 etc... 264 -->24 in total
#multiples of 5 in 274! appearing once = 5,10,15,....270 --> 54 in total

We dont have to worry about 5 appearing twice since largest power of 55 will have to be the largest # of 11's =24

Hence 24 ?

Heman
User avatar
haas_mba07
User avatar
Joined: 02 Jun 2006
Last visit: 26 Jun 2008
Posts: 662
Own Kudos:
218
Posts: 662
Kudos: 218
What is the largest power of 55 that can divide 274! 16 Sep 2006, 19:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
There are two more multiples of 11 between the multiples of 11 you outlined below...

heman
Futuristic
What is the largest power of 55 that can divide 274! ?

55= 11*5

#multiples of 11 in 274! = 11,22,33 etc... 264 -->24 in total
#multiples of 5 in 276! appearing once = 5,10,15,....275 --> 55 in total

We dont have to worry about 5 appearing twice since largest power of 55 will have to be the largest # of 11's =24

Hence 24 ?

Heman
Show more
User avatar
heman
User avatar
Joined: 20 Mar 2006
Last visit: 12 Dec 2006
Posts: 104
Own Kudos:
10
Posts: 104
Kudos: 10
What is the largest power of 55 that can divide 274! 16 Sep 2006, 19:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
trivikram
haas_mba07
hmmm.. I seem to be missing something.

Given

1x2x3.... 274 = 55^k x m

where m is some integer.

As 55 = 11 x 5

The maximum value of k can be the maximum power of 11 (as 11 > 5).

Therefore # of multiples of 11 from 1 to 274
= (264-11)/11 +1 = 24

11 x 22 x 33 x 44... x 264
= 11^24 x 2 x 3 x 4 x .. 24
= 11^24 x 11^2 x K (as there are two more multiples of 11 from 2..24)

=11^26.

This should be 26.. but all options are three digits.

Not sure...

Help futuristic!!! :(

As unrelenting as you can be...Just awesome
Show more


Can you explain this the two more multiples of 11 between 2and 24 are 11& 22 But arent they already accounted for in 11^24 ?

Heman
User avatar
haas_mba07
User avatar
Joined: 02 Jun 2006
Last visit: 26 Jun 2008
Posts: 662
Own Kudos:
218
Posts: 662
Kudos: 218
What is the largest power of 55 that can divide 274! 16 Sep 2006, 19:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
No they are not...

For the multiples of 11 between 1 and 274,

we have 11, 22... 99, 121, 132, 143, 154, 165, 176, 187, 198, 201, 209, 220, 231, 242, 253, 264

From this we take 11 common to get 11^24

i.e. 11^24 x (1,2,3,4,5,6,7,8,9,11,12,13....,24)

In this we have 11 and 22

i.e. 11x24 x 11^2 ( 1,2..5,6...9,10,12,....20,21,23,24)

which gives 11^26.



heman
trivikram
haas_mba07
hmmm.. I seem to be missing something.

Given

1x2x3.... 274 = 55^k x m

where m is some integer.

As 55 = 11 x 5

The maximum value of k can be the maximum power of 11 (as 11 > 5).

Therefore # of multiples of 11 from 1 to 274
= (264-11)/11 +1 = 24

11 x 22 x 33 x 44... x 264
= 11^24 x 2 x 3 x 4 x .. 24
= 11^24 x 11^2 x K (as there are two more multiples of 11 from 2..24)

=11^26.

This should be 26.. but all options are three digits.

Not sure...

Help futuristic!!! :(

As unrelenting as you can be...Just awesome

Can you explain this the two more multiples of 11 between 2and 24 are 11& 22 But arent they already accounted for in 11^24 ?

Heman
Show more
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,957
Own Kudos:
1,117
Posts: 38,957
Kudos: 1,117
What is the largest power of 55 that can divide 274! 03 Dec 2015, 13:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderator:
Bunuel
Math Expert
109740 posts