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

 It is currently 25 Apr 2015, 23:04

### 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

# number prop

Author Message
TAGS:
Intern
Joined: 11 Sep 2009
Posts: 18
Location: Tampa ,FL
Followers: 1

Kudos [?]: 1 [0], given: 2

number prop [#permalink]  27 Oct 2009, 19:49
00:00

Difficulty:

(N/A)

Question Stats:

100% (04:52) correct 0% (00:00) wrong based on 1 sessions
how many different positive integers are factors of 441?

4
6
7
9
11

441=3*3*7*7

So

Can you explain me why these ( 3*3, 7*7 , 3*7 , 3, 7 )are also factors of 441.
Manager
Joined: 11 Sep 2009
Posts: 129
Followers: 4

Kudos [?]: 216 [0], given: 6

Re: number prop [#permalink]  27 Oct 2009, 20:05
The practical way to break it down is to think of the number as a product of factor pairs. You can do this by breaking down the integer into its prime factors:

441 = 3 * 3 * 7 * 7

SO,

441 = (3*3*7*7) * 1 [441, 1]
441 = (3*3*7) * 7 [56, 7]
441 = (3*7*7) * 3 [147, 3]
441 = (3*3) * (7*7) [9, 49]
441 = (3*7) * (3*7) [21]

So there are 9 unique factors.

A much easier method to use when presented with a problem like this is to use the following rule: For each unique prime factor, take the exponent (i.e number of occurances) and add 1. Then multiply these numbers together to determine the number of unique factors. For example,

441 = 3^2 * 7^2

Number of factors = (2+1)(2+1) = 9
Manager
Joined: 15 Sep 2009
Posts: 138
Followers: 1

Kudos [?]: 18 [0], given: 2

Re: number prop [#permalink]  27 Oct 2009, 22:07
441 = 21^2.

441 = (3*7) ^2.

So total no.of factors is 3*3 = 9
Senior Manager
Joined: 18 Aug 2009
Posts: 437
Schools: UT at Austin, Indiana State University, UC at Berkeley
WE 1: 5.5
WE 2: 5.5
WE 3: 6.0
Followers: 6

Kudos [?]: 66 [0], given: 16

Re: number prop [#permalink]  28 Oct 2009, 16:54
I would recommend to use formula for this problem.
1. Factor 441 into prime factors. You will get 3*3, and 7*7
2. We have 3^2 * 7^2
3. So, we multiply (2+1)*(2+1), thus you get 9.
You do not have to calculate each factor of it separately.
_________________

Never give up,,,

Re: number prop   [#permalink] 28 Oct 2009, 16:54
Similar topics Replies Last post
Similar
Topics:
1 number prop 7 30 Jun 2010, 06:01
number prop 4 27 Oct 2009, 14:58
1 number prop 3 14 Sep 2009, 23:41
1 Number prop 6 19 Jan 2009, 16:16
number prop ds 4 14 Apr 2006, 17:48
Display posts from previous: Sort by