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

 It is currently 10 Dec 2013, 18:45

# Events & Promotions

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

# Help: Factors problem !!

Author Message
TAGS:
Intern
Joined: 24 Jul 2010
Posts: 7
Followers: 0

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

Help: Factors problem !! [#permalink]  15 Aug 2010, 02:47
00:00

Difficulty:

5% (low)

Question Stats:

84% (01:23) correct 15% (00:34) wrong based on 19 sessions
How many factors does 36^2 have?
A 2
B 8
C 24
D 25
E 26
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 15109
Followers: 2531

Kudos [?]: 15589 [2] , given: 1563

Re: Help: Factors problem !! [#permalink]  15 Aug 2010, 03:04
2
KUDOS
Expert's post
praveengmat wrote:
How many factors does 36^2 have?
A 2
B 8
C 24
D 25
E 26

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 factors does 36^2 have?

36^2=(2^2*3^2)^2=2^4*3^4 --> # of factors (4+1)*(4+1)=25.

Or another way: 36^2 is a perfect square, # of factors of perfect square is always odd (as perfect square has even powers of its primes and when adding 1 to each and multiplying them as in above formula you'll get the multiplication of odd numbers which is odd). Only odd answer in answer choices is 25.

Hope it helps.
_________________
Intern
Joined: 24 Jul 2010
Posts: 7
Followers: 0

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

Re: Help: Factors problem !! [#permalink]  15 Aug 2010, 03:11
Bunuel wrote:
praveengmat wrote:
How many factors does 36^2 have?
A 2
B 8
C 24
D 25
E 26

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 factors does 36^2 have?

36^2=(2^2*3^2)^2=2^4*3^4 --> # of factors (4+1)*(4+1)=25.

Or another way: 36^2 is a perfect square, # of factors of perfect square is always odd (as perfect square has even powers of its primes and when adding 1 to each and multiplying them as in above formula you'll get the multiplication of odd numbers which is odd). Only odd answer in answer choices is 25.

Hope it helps.

Thanks a ton !!.. loved the approach !
Senior Manager
Joined: 20 Jan 2010
Posts: 278
Schools: HBS, Stanford, Haas, Ross, Cornell, LBS, INSEAD, Oxford, IESE/IE
Followers: 11

Kudos [?]: 113 [1] , given: 117

Re: Help: Factors problem !! [#permalink]  14 Oct 2010, 13:58
1
KUDOS
Factors of a perfect square can be derived by using prime factorization and then using the formula to find perfect square's factors.

In this case (36)^2= (2^2*3^2)^2=2^4*3^4 or (36)^2=(6^2)^2=(6)^4=(2*3)^4=2^4*3^4

And now you can use the formula explained above by Bunuel to determine the answer, which is (4+1)*(4+1)=5*5=25=Odd(Trick is there must be odd number of factors of a perfect square and only 25 is odd in answer choices, so it can be solved within 30 seconds or less )

Please! go through the GMAT Math Book by GMAT CLUB (written by bunuel & walker), all of these tips & tricks are written there. (even I have compiled them in one .pdf file and is shared here on Math forum)
_________________

"Don't be afraid of the space between your dreams and reality. If you can dream it, you can make it so."
Target=780
http://challengemba.blogspot.com
Kudos??

Senior Manager
Joined: 31 Oct 2010
Posts: 493
Location: India
Concentration: Entrepreneurship, Strategy
GMAT 1: 710 Q48 V40
WE: Project Management (Manufacturing)
Followers: 11

Kudos [?]: 19 [0], given: 71

Number of factors [#permalink]  03 Feb 2011, 08:31
How many factors does 36^2 have?
A. 2
B. 8
C. 24
D. 25
E. 26
_________________

My GMAT debrief: from-620-to-710-my-gmat-journey-114437.html

Math Expert
Joined: 02 Sep 2009
Posts: 15109
Followers: 2531

Kudos [?]: 15589 [0], given: 1563

Re: Number of factors [#permalink]  03 Feb 2011, 08:40
Expert's post
Merging similar topics.
_________________
Manager
Joined: 28 Jul 2011
Posts: 214
Followers: 0

Kudos [?]: 20 [0], given: 13

Re: Help: Factors problem !! [#permalink]  29 Aug 2011, 09:57
This method is worth bookmarking. Appreciate it
Manager
Joined: 09 Jun 2011
Posts: 107
Followers: 0

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

Re: Help: Factors problem !! [#permalink]  01 Sep 2011, 19:17
The Easy Answer! (Applicable only in case of perfect square numbers)
A perfect square always have a odd number of factors.
36^2 is a perfect square.
Given the answer choices, the only odd number of factor is 25.

So, The definite answer is D.
Director
Joined: 01 Feb 2011
Posts: 774
Followers: 11

Kudos [?]: 74 [0], given: 42

Re: Help: Factors problem !! [#permalink]  02 Sep 2011, 08:08
36^2 = 2^4 3^4

total factors = (4+1)(4+1) = 25.

Manager
Joined: 20 Nov 2010
Posts: 228
Followers: 4

Kudos [?]: 5 [0], given: 38

Re: Help: Factors problem !! [#permalink]  03 Sep 2011, 10:04
The odd number of factors for perfect squares solves this in no time. Nice trick.
_________________

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
MGMAT 6 650 (51,31) on 31/8/11
MGMAT 1 670 (48,33) on 04/9/11
MGMAT 2 670 (47,34) on 07/9/11
MGMAT 3 680 (47,35) on 18/9/11
GMAT Prep1 680 ( 50, 31) on 10/11/11

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
CR notes
http://gmatclub.com/forum/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142
http://gmatclub.com/forum/1001-ds-questions-file-106193.html#p832133
http://gmatclub.com/forum/gmat-prep-critical-reasoning-collection-106783.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html?hilit=chineseburned

Re: Help: Factors problem !!   [#permalink] 03 Sep 2011, 10:04
Similar topics Replies Last post
Similar
Topics:
Factoring problem 3 04 Feb 2007, 17:27
2 prime factor problem 3 09 Jun 2009, 19:46
1 Factoring problem 6 19 Jul 2010, 15:54
1 Factorization Problem 7 17 Jan 2011, 18:35
Display posts from previous: Sort by