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

 It is currently 24 Sep 2018, 10:35

### 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

# How many factors of the number 2^6*3^5*5^4*6^3 are multiples of 360?

Author Message
TAGS:

### Hide Tags

Retired Moderator
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 526
How many factors of the number 2^6*3^5*5^4*6^3 are multiples of 360?  [#permalink]

### Show Tags

20 Oct 2017, 07:35
2
00:00

Difficulty:

45% (medium)

Question Stats:

67% (02:18) correct 33% (02:03) wrong based on 39 sessions

### HideShow timer Statistics

How many factors of the number $$2^6*3^5*5^4*6^3$$ are multiples of 360?

A. 36
B. 108
C. 144
D. 196
E. 288

_________________

Hasan Mahmud

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
How many factors of the number 2^6*3^5*5^4*6^3 are multiples of 360?  [#permalink]

### Show Tags

20 Oct 2017, 07:44
1
2
Mahmud6 wrote:
How many factors of the number $$2^6*3^5*5^4*6^3$$ are multiples of 360?

A. 36
B. 1088
C. 144
D. 196
E. 288

$$2^6*3^5*5^4*6^3=2^9*3^8*5^4$$

$$360=2^3*3^2*5$$

all factors of $$2^9*3^8*5^4$$ that can be written as multiples of $$360$$ will be of the form $$2^3*3^2*5*p$$

therefore $$2^9*3^8*5^4=2^3*3^2*5*p$$

or $$p= 2^6*3^6*5^3$$

Now the number of factors of $$p=(1+6)*(1+6)*(1+3)=196$$

Option D
Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3672
How many factors of the number 2^6*3^5*5^4*6^3 are multiples of 360?  [#permalink]

### Show Tags

20 Oct 2017, 07:47
To find out the number of multiples of 360, let's first find out its factors and then take them out of the total factors. This will ensure that the remaining factors will always include the factors of 360.

Let's solve now:

360 = 9 * 4 * 10 = $$3^2*2^3*5^1$$

That means let's take two 3s, three 2s and one 5 out of the original number.

$$2^6*3^5*5^4*6^3$$

After taking the required factors out, we are left with : $$2^3*3^3*5^3*6^3$$

As per the formula, $$a^p*b^q*c^r$$, we have number of factors = (p+1)(q+1)(r+1), where a,b and c MUST be distinct primes.

Let's prime factorise all and club the common number, I will have the number as $$2^6*3^6*5^4$$ [Confused? Just split take 6 = 2*3 and then join 2 with existing 2s and 3 with existing 3s]

Therefore, for our question I can say, number of factors multiple of 360 = (6+1) ( 6+1)(3+1) = 49*4 = 196

_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.

Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free

How many factors of the number 2^6*3^5*5^4*6^3 are multiples of 360? &nbs [#permalink] 20 Oct 2017, 07:47
Display posts from previous: Sort by

# How many factors of the number 2^6*3^5*5^4*6^3 are multiples of 360?

## Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne 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®.