GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Nov 2019, 04:05 ### 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

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.  # If n is the greatest positive integer for which 2^n is a factor of 10!

Author Message
TAGS:

### Hide Tags

Intern  Joined: 21 Jul 2012
Posts: 8
If n is the greatest positive integer for which 2^n is a factor of 10!  [#permalink]

### Show Tags

4
14 00:00

Difficulty:

(N/A)

Question Stats: 84% (00:46) correct 16% (01:12) wrong based on 429 sessions

### HideShow timer Statistics

If n is the greatest positive integer for which 2^n is a factor of 10!, then n =?

A. 2
B. 4
C. 6
D. 8
E. 10

Is any one can provide a solution for this question?It's from GWD. Thanks!
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15503
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If n is the greatest positive integer for which 2^n is a factor of 10!  [#permalink]

### Show Tags

6
2
Hi All,

Many Test Takers get these types of questions wrong because they move too quickly through the work and don't do enough work on their pads. It's a relatively straight-forward prompt though...

We're essentially asked to find all the "2"s inside 10!

The 'key' to this question is to realize that some values have MORE THAN ONE 2 in them....

10! = (10)(9)(8)(7)(6)(5)(4)(3)(2)(1)

10 = 5x2 --> one 2
8 = 2x2x2 --> three 2s
6 = 3x2 --> one 2
4 = 2x2 --> two 2s
2 = 1x2 --> one 2

1+3+1+2+1 = eight 2s

GMAT assassins aren't born, they're made,
Rich
_________________
Director  Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 990
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Re: If n is the greatest positive integer for which 2^n is a factor of 10!  [#permalink]

### Show Tags

3
6
In the questions where you are supposed to find out the maximum power of a prime factor which is a factor of n!, keep one only on thing in mind:
Let the prime number you are looking for be x, then:
$$n/x + n/x^2 + n/x^3.........n/x^k$$ where $$x^k$$ <=n.
If you apply this rule here,
$$10/2 +10/2^2 +10/2^3$$ or 5+2+1=8.
Hence maximum power of 2 in $$10!$$ will be 8.
_________________
##### General Discussion
Math Expert V
Joined: 02 Sep 2009
Posts: 59263
Re: If n is the greatest positive integer for which 2^n is a factor of 10!  [#permalink]

### Show Tags

curtis0063 wrote:
If n is the greatest positive integer for which 2^n is a factor of 10!, then n =?

A. 2
B. 4
C. 6
D. 8
E. 10

Is any one can provide a solution for this question?It's from GWD. Thanks!

_________________
Manager  Joined: 20 Dec 2013
Posts: 223
Location: India
Re: If n is the greatest positive integer for which 2^n is a factor of 10!  [#permalink]

### Show Tags

We can count the total number of powers of 2 in 10!
There are 8 of them.So answer D.

Posted from my mobile device
Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4835
Location: India
GPA: 3.5
Re: If n is the greatest positive integer for which 2^n is a factor of 10!  [#permalink]

### Show Tags

1
curtis0063 wrote:
If n is the greatest positive integer for which 2^n is a factor of 10!, then n =?

A. 2
B. 4
C. 6
D. 8
E. 10

Is any one can provide a solution for this question?It's from GWD. Thanks!

$$\frac{10}{2}$$ = 5
$$\frac{5}{2}$$ = 2
$$\frac{2}{2}$$ = 1

Now, 5+2+1 = 8

Hence the highest power of 2 that will divide 10! is 8
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Intern  B
Joined: 27 Jul 2017
Posts: 47
Re: If n is the greatest positive integer for which 2^n is a factor of 10!  [#permalink]

### Show Tags

The answer must be D, i.e. 2 will be having a total power of 8 in 10!
_________________
Ujjwal
Sharing is Gaining!
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2812
Re: If n is the greatest positive integer for which 2^n is a factor of 10!  [#permalink]

### Show Tags

curtis0063 wrote:
If n is the greatest positive integer for which 2^n is a factor of 10!, then n =?

A. 2
B. 4
C. 6
D. 8
E. 10

Let’s put the even numbers from 2 to 10 in prime factors.

2

4 = 2^2

6 = 2 x 3

8 = 2^3

10 = 2 x 5

We see that there are 8 prime factors of 2 in 10!, so 8 is the value of n.

Alternate Solution:

We know that 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. Let’s find all the 2’s in this product.

The number 10 contributes 1 two.

The number 8 contributes 3 twos.

The number 6 contributes 1 two.

The number 4 contributes 2 twos.

The number 2 contributes 1 two.

Thus, we have a total of 8 twos, and so 8 is the value of n..

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User Joined: 09 Sep 2013
Posts: 13629
Re: If n is the greatest positive integer for which 2^n is a factor of 10!  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: If n is the greatest positive integer for which 2^n is a factor of 10!   [#permalink] 02 May 2019, 04:40
Display posts from previous: Sort by

# If n is the greatest positive integer for which 2^n is a factor of 10!  