Find all School-related info fast with the new School-Specific MBA Forum

It is currently 22 Jul 2014, 19:45

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

number of terminal zeros

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Joined: 26 Dec 2008
Posts: 58
Schools: Booth (Admit R1), Sloan (Ding R1), Tuck (R1)
Followers: 2

Kudos [?]: 7 [0], given: 0

number of terminal zeros [#permalink] New post 05 Mar 2009, 07:27
how many zeros are there at the end of 100!

a. 10
b. 20
c. 24
d. 28
e. 30

I thought this problem was pretty interesting so sharing it here. I will reveal the answer and approach after I get a few replies.
Current Student
avatar
Joined: 28 Dec 2004
Posts: 3405
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 149 [0], given: 2

GMAT Tests User
Re: number of terminal zeros [#permalink] New post 05 Mar 2009, 07:55
i get 24..

2^a 5^b ...breakdown the 100! to its prime factor, the power 5 determines the numbers of zeros..
Senior Manager
Senior Manager
avatar
Joined: 30 Nov 2008
Posts: 494
Schools: Fuqua
Followers: 10

Kudos [?]: 119 [0], given: 15

GMAT Tests User
Re: number of terminal zeros [#permalink] New post 05 Mar 2009, 08:35
FN wrote:
i get 24..

2^a 5^b ...breakdown the 100! to its prime factor, the power 5 determines the numbers of zeros..


This sounds a better approach. But can you please elaborate how you came with the power of 5 to be 24?
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 30 Nov 2008
Posts: 494
Schools: Fuqua
Followers: 10

Kudos [?]: 119 [1] , given: 15

GMAT Tests User
Re: number of terminal zeros [#permalink] New post 05 Mar 2009, 09:54
1
This post received
KUDOS
Never mind. I figured it out.

1. in 100!, we have 100 / 5 numbers that have 5 as the prime factor. So we get a count of 20.

2. Now 25 integer have an additoinal 5 as a factor. So 100 / 25 gives an additional 5 as the prime factor. So we get a count of 4.

Now we have the power of 5 to be 20 + 4 which is 24.

-----------------------------------------------------------------------------------------------------------------------------------

Simple Rule worth noting to find the number of terminating zeroes of n!

1. Divide the number n by 5^m where m ranges from 1 thru a max value x such that 5^x is less than the number.
2. Sum of all the quotients obtained is the Ans.


For in our case n = 100.

Divide 100 by 5, 5^2. Quotients are 20 and 4. So the final ans is 24.

another example for 200!.

200 / 5 = 40
200 / 25 = 8
200 / 125 = 1. (Stop at this point. 5^4 = 625 < 200 and division results zero from here onwards. )

So ans is 49.

Some good alternatives are provided in the below link.

Edit: URL was broken

Last edited by mrsmarthi on 05 Mar 2009, 10:47, edited 1 time in total.
Director
Director
avatar
Joined: 01 Aug 2008
Posts: 770
Followers: 3

Kudos [?]: 74 [0], given: 99

GMAT Tests User
Re: number of terminal zeros [#permalink] New post 05 Mar 2009, 10:26
good explanation mrsmarthi . +1 for you.

Thanks.
Manager
Manager
User avatar
Joined: 26 Dec 2008
Posts: 58
Schools: Booth (Admit R1), Sloan (Ding R1), Tuck (R1)
Followers: 2

Kudos [?]: 7 [0], given: 0

Re: number of terminal zeros [#permalink] New post 05 Mar 2009, 11:19
mrsmarthi wrote:
Never mind. I figured it out.

1. in 100!, we have 100 / 5 numbers that have 5 as the prime factor. So we get a count of 20.

2. Now 25 integer have an additoinal 5 as a factor. So 100 / 25 gives an additional 5 as the prime factor. So we get a count of 4.

Now we have the power of 5 to be 20 + 4 which is 24.

-----------------------------------------------------------------------------------------------------------------------------------

Simple Rule worth noting to find the number of terminating zeroes of n!

1. Divide the number n by 5^m where m ranges from 1 thru a max value x such that 5^x is less than the number.
2. Sum of all the quotients obtained is the Ans.


For in our case n = 100.

Divide 100 by 5, 5^2. Quotients are 20 and 4. So the final ans is 24.

another example for 200!.

200 / 5 = 40
200 / 25 = 8
200 / 125 = 1. (Stop at this point. 5^4 = 625 < 200 and division results zero from here onwards. )

So ans is 49.

Some good alternatives are provided in the below link.

Edit: URL was broken


Right approach and answer. Good show!

Didn't realize someone had posted this question already.
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 24 Feb 2007
Posts: 267
Location: nj
Followers: 1

Kudos [?]: 27 [1] , given: 2

GMAT Tests User
Re: number of terminal zeros [#permalink] New post 05 Mar 2009, 12:54
1
This post received
KUDOS
mrsmarthi wrote:
Never mind. I figured it out.

1. in 100!, we have 100 / 5 numbers that have 5 as the prime factor. So we get a count of 20.

2. Now 25 integer have an additoinal 5 as a factor. So 100 / 25 gives an additional 5 as the prime factor. So we get a count of 4.

Now we have the power of 5 to be 20 + 4 which is 24.

-----------------------------------------------------------------------------------------------------------------------------------

Simple Rule worth noting to find the number of terminating zeroes of n!

1. Divide the number n by 5^m where m ranges from 1 thru a max value x such that 5^x is less than the number.
2. Sum of all the quotients obtained is the Ans.


For in our case n = 100.

Divide 100 by 5, 5^2. Quotients are 20 and 4. So the final ans is 24.

another example for 200!.

200 / 5 = 40
200 / 25 = 8
200 / 125 = 1. (Stop at this point. 5^4 = 625 < 200 and division results zero from here onwards. )

So ans is 49.

Some good alternatives are provided in the below link.

Edit: URL was broken



Just an application of the above solution

this kind of question can also be put like:

what power of 15 divides 87! exactly.

15 = 3*5


87/5 + 87/5^2 = 17 + 3 = 20

87/3 + 87/3^2 +87/3^3 +87/3^4 +.. = 29 (more than 20)

so 20 is the answer.
Re: number of terminal zeros   [#permalink] 05 Mar 2009, 12:54
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic Question on terminating zero's? fozzzy 2 16 Jun 2013, 01:21
2 Terminating Zeros enigma123 2 26 Dec 2011, 10:31
1 terminating Zeros rishi2377 5 17 Oct 2008, 10:05
PS: terminating zeros Himalayan 3 08 Jun 2007, 22:48
3 How many terminating zeroes does 200! have? TS 5 15 Apr 2005, 05:42
Display posts from previous: Sort by

number of terminal zeros

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.