Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 25 May 2017, 00:48

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# m02#24

Author Message
Retired Moderator
Joined: 18 Jul 2008
Posts: 975
Followers: 10

Kudos [?]: 219 [1] , given: 5

### Show Tags

05 Nov 2008, 08:21
1
KUDOS
2
This post was
BOOKMARKED
How many distinct integers are factors of 90?

(A) 6
(B) 8
(C) 9
(D) 10
(E) 12

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

I don't quite agree with the OA.
Manager
Joined: 17 Apr 2010
Posts: 102
Followers: 2

Kudos [?]: 57 [26] , given: 12

### Show Tags

09 Jul 2010, 06:43
26
KUDOS
3
This post was
BOOKMARKED
To know the number of number of factors for a number , we need to split the number in the following way

Number = a^x * b^y * c^z .......so on

The number of factors would be (x+1)*(y+1)*(z+1)...so on

Applying the above to the current example

90 = 2^1 * 3^2 * 5^1

The number of factors = (1+1) * (2+1) * (1+1) = 2*3*2 = 12

Please send kudos if you like this
Manager
Status: Waiting to hear from University of Texas at Austin
Joined: 24 May 2010
Posts: 76
Location: Changchun, China
Schools: University of Texas at Austin, Michigan State
Followers: 5

Kudos [?]: 62 [3] , given: 4

### Show Tags

10 Jul 2010, 03:17
3
KUDOS
Possibly Correct, Could someone tell me for sure

First we factor 90 into primes 3*3*5*2

I thought of this as a combination problem with a duplicate choice 4! / 2 !

4! because I have to put the numbers in order A*B*C*D

2! because I have a duplicate choice (3)

Can anyone tell me if this will work for other situations?
or did I just confuse myself and everyone else?

Alternatively, I write these questions out starting with the largest and smallest factor
(I am using the .... to show that I write them a good distance apart on my scratch paper.)
1 .............................................................................................................. 90
next
1, 2,...........................................................................45, 90
1, 2, 3 30, 45, 90
1, 2, 3, 5, 18, 30, 45, 90
If find that doing things this way prevents me from having duplicates and quickly gets me to a situation where I know I have covered all the possibilities.
This method is really only good for number less than 100. For example if you had 87452, it might take too much time to do this.
Director
Joined: 21 Dec 2009
Posts: 585
Concentration: Entrepreneurship, Finance
Followers: 18

Kudos [?]: 704 [2] , given: 20

### Show Tags

16 Jul 2010, 02:43
2
KUDOS
90, when prime-factorized, can be expressed as: 2*(3^2)*5
i.e (2^1)(3^2)(5^1).
generally, distinct factors [of N = (a^x)(b^y)(c^z)]
is (x+1)(y+1)(z+1)

so, for 90, the distinct prime factors = 2*3*2 = 12
OA = E.
_________________

KUDOS me if you feel my contribution has helped you.

Math Expert
Joined: 02 Sep 2009
Posts: 38859
Followers: 7728

Kudos [?]: 106073 [2] , given: 11607

### Show Tags

17 Jul 2013, 05:55
2
KUDOS
Expert's post
Finding the Number of Factors of an Integer

First make prime factorization of an integer $$n=a^p*b^q*c^r$$, where $$a$$, $$b$$, and $$c$$ are prime factors of $$n$$ and $$p$$, $$q$$, and $$r$$ are their powers.

The number of factors of $$n$$ will be expressed by the formula $$(p+1)(q+1)(r+1)$$. NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: $$450=2^1*3^2*5^2$$

Total number of factors of 450 including 1 and 450 itself is $$(1+1)*(2+1)*(2+1)=2*3*3=18$$ factors.

Back to the original question:

How many distinct integers are factors of 90?

A. 6
B. 8
C. 9
D. 10
E. 12

$$90=2*3^2*5$$, which means that the number of factors of 90 is: $$(1+1)(2+1)(1+1)=12$$.

Similar questions to practice:
how-many-odd-positive-divisors-does-540-have-106082.html
how-many-factors-does-36-2-have-126422.html
how-many-different-positive-integers-are-factor-of-130628.html
how-many-distinct-positive-factors-does-30-030-have-144326.html

Hope it helps.
_________________
Intern
Joined: 17 May 2010
Posts: 19
Followers: 0

Kudos [?]: 4 [1] , given: 0

### Show Tags

10 Jul 2010, 05:48
1
KUDOS
E

I found a very useful formula (from GMAT Club forum) number of factors of a^x*b^y*c^z = (x+1)(y+1)(z+1).

Do hope it helps.
SVP
Joined: 17 Jun 2008
Posts: 1553
Followers: 11

Kudos [?]: 264 [0], given: 0

### Show Tags

05 Nov 2008, 09:37
Is OA not 12?

90 = 9*10 = 2*3*3*5

distinct factors:
1, 2, 3, 5,
3*3, 3*2, 3*5, 2*5,
3*3*2, 3*3*5, 3*2*5,
3*3*2*5
Retired Moderator
Joined: 18 Jul 2008
Posts: 975
Followers: 10

Kudos [?]: 219 [0], given: 5

### Show Tags

05 Nov 2008, 09:51
The OA is 12.

the factors are 90, 45, 30, 18, 15, 10, 9, 6, 5, 3, 2, 1

But wouldn't "distinct integers" mean only 1,2,3,6,5,9? Hence 6...
SVP
Joined: 17 Jun 2008
Posts: 1553
Followers: 11

Kudos [?]: 264 [0], given: 0

### Show Tags

05 Nov 2008, 12:16
The question is asking for "distinct integers as factors". I guess you read it as "distinct digits as factors".
Retired Moderator
Joined: 18 Jul 2008
Posts: 975
Followers: 10

Kudos [?]: 219 [0], given: 5

### Show Tags

05 Nov 2008, 12:31
Ahh there's my problem! Thanks.
Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 408
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Followers: 8

Kudos [?]: 211 [0], given: 50

### Show Tags

16 Jul 2010, 18:32
I have been going through some of the materials from MGMAT. I would go about solving this problem this way....

90 -- 3^2*2^1*5^1

Number of factors would be (2+1)(1+1)(1+1) = 12.

I believe that this is the quick way of solving these problems....

Are there any other quick ways to solve these kinds of problems ?????
_________________

Support GMAT Club by putting a GMAT Club badge on your blog

Intern
Joined: 23 Jun 2010
Posts: 36
Followers: 0

Kudos [?]: 28 [0], given: 5

### Show Tags

02 Aug 2010, 15:07
tiruraju wrote:
To know the number of number of factors for a number , we need to split the number in the following way

Number = a^x * b^y * c^z .......so on

The number of factors would be (x+1)*(y+1)*(z+1)...so on

Applying the above to the current example

90 = 2^1 * 3^2 * 5^1

The number of factors = (1+1) * (2+1) * (1+1) = 2*3*2 = 12

Please send kudos if you like this

This is definitely a more methodical approach to the question. But it requires double the work. Since you anyways have to prime factor number N, I found it easier to factorize the non-prime factor further until it is represented as prime. For example, 90 = 45 x 2. Then 45 = 15 x 3. 15 = 5 x 3 and so on. At the end it is a simple math of counting the factors!
_________________

-DK
---------------------------------------------------------
If you like what you read then give a Kudos!
Diagnostic Test: 620
The past is a guidepost, not a hitching post.
---------------------------------------------------------

Intern
Joined: 30 Aug 2009
Posts: 26
Followers: 0

Kudos [?]: 4 [0], given: 3

### Show Tags

11 Aug 2010, 23:47
tiruraju wrote:
To know the number of number of factors for a number , we need to split the number in the following way

Number = a^x * b^y * c^z .......so on

The number of factors would be (x+1)*(y+1)*(z+1)...so on

Applying the above to the current example

90 = 2^1 * 3^2 * 5^1

The number of factors = (1+1) * (2+1) * (1+1) = 2*3*2 = 12

Please send kudos if you like this

This is very useful if you have to determine the number of factors of very large numbers (kudos!). Finding each factor by trial-and-error would cost way to much time. Try 2496: prime factorization is much easier (2^5)*3*13 -> (5+1)*(1+1)*(1+1)=24
Senior Manager
Joined: 17 May 2010
Posts: 291
GMAT 1: 710 Q47 V40
Followers: 4

Kudos [?]: 53 [0], given: 7

### Show Tags

13 Jul 2011, 05:52
I wrote all the factors out and got 10. I forgot to add 1 and 90 as factors. Grrrr!!
_________________

If you like my post, consider giving me KUDOS!

Intern
Joined: 07 Jul 2011
Posts: 1
Followers: 0

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

### Show Tags

13 Jul 2011, 11:43
I got the correct answer, (E): 12 however I do have one question, do negative integers not qualify as "distinct" factors? Meaning the answer would be 12 positive distinct factors + 12 negative distinct factors = 24 distinct factors in total?
Re: m02#24   [#permalink] 13 Jul 2011, 11:43
Display posts from previous: Sort by

# m02#24

Moderator: Bunuel

 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®.