How many different positive integers are factors of 441 : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 24 Jan 2017, 18:49

### 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

# How many different positive integers are factors of 441

Author Message
TAGS:

### Hide Tags

Intern
Joined: 27 Mar 2012
Posts: 17
Followers: 0

Kudos [?]: 35 [1] , given: 1

How many different positive integers are factors of 441 [#permalink]

### Show Tags

13 Apr 2012, 01:42
1
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

65% (01:44) correct 35% (01:06) wrong based on 339 sessions

### HideShow timer Statistics

How many different positive integers are factors of 441

A. 4
B. 6
C. 7
D. 9
E. 11

Can this be solved using the method of (p+1) * (q+1) * (r+1) when the given no is of the prime no of the form N=a^p b^q c^r where a,b,c are prime factors ? Can you please clarify whether my approach is correct?
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Apr 2012, 05:37, edited 2 times in total.
Edited the question
Intern
Joined: 18 Sep 2011
Posts: 20
GMAT Date: 11-09-2011
Followers: 0

Kudos [?]: 1 [0], given: 6

Re: How many different positive integers are factor of 441 ? [#permalink]

### Show Tags

13 Apr 2012, 03:55
Yeah you are absolutely right!

Powers of prime factors adding one on to it and multiply

(2+1)*(2+1)=9

Posted from my mobile device
Manager
Joined: 06 Feb 2012
Posts: 91
WE: Project Management (Other)
Followers: 3

Kudos [?]: 53 [0], given: 16

Re: How many different positive integers are factor of 441 ? [#permalink]

### Show Tags

13 Apr 2012, 05:27
sugu86 wrote:
How many different positive integers are factor of 441 ? (A) 4 (B) 6 (C) 7 (D) 9 (E) 11. OA is D. Can this be solved using the method of (p+1) * (q+1) * (r+1) when the given no is of the prime no of the form N=a^p b^q c^r where a,b,c are prime factors ? Can you please clarify whether my approach is correct?

Could you indicate where you found that method? I have not heard of it and I am curious b/c it may be faster than the way I usually approach prime factorization problems....

Usually check if the number is divisible by 2, then 5, then 3, etc... (7, 11, 13,17, ....)
Here 441 is:
- clearly not divisible by 2 or 5 (not even or ending with a 5 or 0)
- divisible by 3 (sum of the digits is 4+4+1=9 divisible by 3)
441 = 3 * 100 + 141 = 3 * 100 + 120 + 21 = 3 *(100+40+7) = 3 * 147 (I would do the middle step in my head so to speak)
same thing with 147
147 = 120 + 27 = 3 * 49
and 49 = 7^2

so 441 = 3^2 * 7^2

Note that I found those links interesting:
http://www.f1gmat.com/data-sufficiency/ ... ility-rule (Not specific to GMAT)
Jeff Sackmann - specific to GMAT strategies:
http://www.gmathacks.com/mental-math/factor-faster.html
http://www.gmathacks.com/gmat-math/numb ... teger.html
http://www.gmathacks.com/main/mental-math.html (general tricks)
_________________

Kudos is a great way to say Thank you...

Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93673 [7] , given: 10583

Re: How many different positive integers are factors of 441 [#permalink]

### Show Tags

13 Apr 2012, 05:43
7
KUDOS
Expert's post
5
This post was
BOOKMARKED
sugu86 wrote:
How many different positive integers are factors of 441

A. 4
B. 6
C. 7
D. 9
E. 11

Can this be solved using the method of (p+1) * (q+1) * (r+1) when the given no is of the prime no of the form N=a^p b^q c^r where a,b,c are prime factors ? Can you please clarify whether my approach is correct?

MUST KNOW FOR GMAT:

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.

For more on these issues check Number Theory chapter of Math Book: math-number-theory-88376.html

BACK TO THE ORIGINAL QUESTION.

How many different positive integers are factors of 441
A. 4
B. 6
C. 7
D. 9
E. 11

Make prime factorization of 441: 441=3^2*7^2, hence it has (2+1)(2+1)=9 different positive factors.

Hope it helps.
_________________
Manager
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 235
Schools: Johnson '15
Followers: 2

Kudos [?]: 50 [0], given: 16

Re: How many different positive integers are factor of 441 ? [#permalink]

### Show Tags

14 Apr 2012, 00:00
GreginChicago wrote:
sugu86 wrote:
How many different positive integers are factor of 441 ? (A) 4 (B) 6 (C) 7 (D) 9 (E) 11. OA is D. Can this be solved using the method of (p+1) * (q+1) * (r+1) when the given no is of the prime no of the form N=a^p b^q c^r where a,b,c are prime factors ? Can you please clarify whether my approach is correct?

Could you indicate where you found that method? I have not heard of it and I am curious b/c it may be faster than the way I usually approach prime factorization problems....

Usually check if the number is divisible by 2, then 5, then 3, etc... (7, 11, 13,17, ....)
Here 441 is:
- clearly not divisible by 2 or 5 (not even or ending with a 5 or 0)
- divisible by 3 (sum of the digits is 4+4+1=9 divisible by 3)
441 = 3 * 100 + 141 = 3 * 100 + 120 + 21 = 3 *(100+40+7) = 3 * 147 (I would do the middle step in my head so to speak)
same thing with 147
147 = 120 + 27 = 3 * 49
and 49 = 7^2

so 441 = 3^2 * 7^2

Note that I found those links interesting:
http://www.f1gmat.com/data-sufficiency/ ... ility-rule (Not specific to GMAT)
Jeff Sackmann - specific to GMAT strategies:
http://www.gmathacks.com/mental-math/factor-faster.html
http://www.gmathacks.com/gmat-math/numb ... teger.html
http://www.gmathacks.com/main/mental-math.html (general tricks)

is 441 = 7 * 7 * 2 * 2...i think 441 cant be divided by 2

should it not be 7 * 7 * 3 * 3
_________________

Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

Satyameva Jayate - Truth alone triumphs

Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93673 [0], given: 10583

Re: How many different positive integers are factor of 441 ? [#permalink]

### Show Tags

14 Apr 2012, 01:13
harshavmrg wrote:
GreginChicago wrote:
sugu86 wrote:
How many different positive integers are factor of 441 ? (A) 4 (B) 6 (C) 7 (D) 9 (E) 11. OA is D. Can this be solved using the method of (p+1) * (q+1) * (r+1) when the given no is of the prime no of the form N=a^p b^q c^r where a,b,c are prime factors ? Can you please clarify whether my approach is correct?

Could you indicate where you found that method? I have not heard of it and I am curious b/c it may be faster than the way I usually approach prime factorization problems....

Usually check if the number is divisible by 2, then 5, then 3, etc... (7, 11, 13,17, ....)
Here 441 is:
- clearly not divisible by 2 or 5 (not even or ending with a 5 or 0)
- divisible by 3 (sum of the digits is 4+4+1=9 divisible by 3)
441 = 3 * 100 + 141 = 3 * 100 + 120 + 21 = 3 *(100+40+7) = 3 * 147 (I would do the middle step in my head so to speak)
same thing with 147
147 = 120 + 27 = 3 * 49
and 49 = 7^2

so 441 = 3^2 * 7^2

Note that I found those links interesting:
http://www.f1gmat.com/data-sufficiency/ ... ility-rule (Not specific to GMAT)
Jeff Sackmann - specific to GMAT strategies:
http://www.gmathacks.com/mental-math/factor-faster.html
http://www.gmathacks.com/gmat-math/numb ... teger.html
http://www.gmathacks.com/main/mental-math.html (general tricks)

is 441 = 7 * 7 * 2 * 2...i think 441 cant be divided by 2

should it not be 7 * 7 * 3 * 3

GreginChicago is saying exactly the same thing!

Check for a solution here: how-many-different-positive-integers-are-factor-of-130628.html#p1073364
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13550
Followers: 578

Kudos [?]: 163 [0], given: 0

Re: How many different positive integers are factors of 441 [#permalink]

### Show Tags

17 Mar 2014, 03:00
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.
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 47

Kudos [?]: 1939 [0], given: 193

Re: How many different positive integers are factors of 441 [#permalink]

### Show Tags

27 Mar 2014, 20:02
$$441 = 21^2$$

$$= (7 * 3)^2$$

$$= 7^2 . 3^2$$

Prime factors = (2+1) * (2+1) = 9

_________________

Kindly press "+1 Kudos" to appreciate

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13550
Followers: 578

Kudos [?]: 163 [0], given: 0

Re: How many different positive integers are factors of 441 [#permalink]

### Show Tags

29 May 2015, 08:45
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13550
Followers: 578

Kudos [?]: 163 [0], given: 0

Re: How many different positive integers are factors of 441 [#permalink]

### Show Tags

15 Aug 2016, 03:28
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: How many different positive integers are factors of 441   [#permalink] 15 Aug 2016, 03:28
Similar topics Replies Last post
Similar
Topics:
2 How many different positive even integers are factors of 294? 6 29 Dec 2016, 11:14
How many diferent positive integers are factors of 225 ? 2 26 Apr 2015, 19:23
1 How many different positive integers can be formed 5 24 Feb 2015, 10:42
10 The positive integer 200 has how many factors? 11 17 Sep 2012, 05:24
8 How many of the positive factors of 42 are not factors of 56? 14 07 Aug 2011, 06:18
Display posts from previous: Sort by