Last visit was: 17 May 2024, 17:45 It is currently 17 May 2024, 17:45
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Finding Factors of Large Nums

User avatar
amenewyork
Intern
Intern
Joined: 21 Jan 2010
Posts: 2
Own Kudos [?]: 1 [1]
Given Kudos: 1
Concentration: Technology Management, MIS
Send PM
Finding Factors of Large Nums [#permalink] Finding Factors of Large Nums   02 Mar 2010, 13:21
1
Kudos
Hi everyone, I'm beginning my GMAT Quant journey with the MGMAT Number Properties guide and the Kaplan Math Workbook (6th ed.). I understand the concept of factoring, finding GCFs, etc, but I'm wondering if there is a quick/tried-and-true strategy for finding factors of large numbers without having to create a chart, which seems too time consuming. Thanks in advance for the help!



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
firasath
Intern
Intern
Joined: 04 Feb 2007
Posts: 49
Own Kudos [?]: 180 [1]
Given Kudos: 16
Send PM
Re: Finding Factors of Large Nums [#permalink] Finding Factors of Large Nums   02 Mar 2010, 18:16
1
Kudos
amenewyork wrote:
Hi everyone, I'm beginning my GMAT Quant journey with the MGMAT Number Properties guide and the Kaplan Math Workbook (6th ed.). I understand the concept of factoring, finding GCFs, etc, but I'm wondering if there is a quick/tried-and-true strategy for finding factors of large numbers without having to create a chart, which seems too time consuming. Thanks in advance for the help!


Not sure what your "chart" method is but an easy method to remember and use is to find the prime factorization and then expand the permutations of the exponents:

example:

196

196 = 2^2*7^2 (prime factorization)


To determine how many factors there are, just look at each power, add one, and multiply together.

(2 + 1)(2 + 1)
(3)(3)
9 factors

now work through the permutations of the exponents starting with 0:

2^0*7^0 = 1*1 = 1
2^0*7^1 = 1*7 = 7
2^0*7^2 = 1*49= 49

2^1*7^0 = 2*1=2
2^1*7^1 = 2*7=14
2^1*7^2 = 2*49 = 98

2^2*7^0 = 4*1=4
2^2*7^1 = 4*7=28
2^2*7^2 = 4*49 = 196

thus, the factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196
User avatar
amenewyork
Intern
Intern
Joined: 21 Jan 2010
Posts: 2
Own Kudos [?]: 1 [0]
Given Kudos: 1
Concentration: Technology Management, MIS
Send PM
Re: Finding Factors of Large Nums [#permalink] Finding Factors of Large Nums   04 Mar 2010, 08:56
Great, thank you for that method!
User avatar
AshForGMAT
Manager
Manager
Joined: 19 Jul 2009
Status:Applying
Posts: 87
Own Kudos [?]: 20 [0]
Given Kudos: 6
Location: United Kingdom
Concentration: General Management, Strategy
Schools: Fuqua '14 (D) Kellogg '14 (D) Ross '14 (WL) Kenan-Flagler '14 (A)
GPA: 3.65
WE:Consulting (Telecommunications)
Send PM
Re: Finding Factors of Large Nums [#permalink] Finding Factors of Large Nums   05 Mar 2010, 05:15
Yes the above method is the shortest method that i have come across...

Please share if you have come across anything shorter !
User avatar
tarun
Manager
Manager
Joined: 30 Jun 2004
Posts: 105
Own Kudos [?]: 99 [0]
Given Kudos: 5
Location: Singapore
Send PM
GMAT ToolKit User
Re: Finding Factors of Large Nums [#permalink] Finding Factors of Large Nums   09 Mar 2010, 04:15
I agree. This is the shortest method.
User avatar
fruit
Intern
Intern
Joined: 21 Feb 2010
Posts: 14
Own Kudos [?]: 14 [0]
Given Kudos: 9
Location: Ukraine
Send PM
Re: Finding Factors of Large Nums [#permalink] Finding Factors of Large Nums   09 Mar 2010, 14:16
Thanks for this method.
And what about the number 483?
We get three prime numbers 7, 23 and 3. What to do next?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93334
Own Kudos [?]: 624545 [0]
Given Kudos: 81898
Send PM
CAT Tests Forum Quiz Mode
Re: Finding Factors of Large Nums [#permalink] Finding Factors of Large Nums   10 Mar 2010, 03:16
Expert Reply
amenewyork wrote:
Hi everyone, I'm beginning my GMAT Quant journey with the MGMAT Number Properties guide and the Kaplan Math Workbook (6th ed.). I understand the concept of factoring, finding GCFs, etc, but I'm wondering if there is a quick/tried-and-true strategy for finding factors of large numbers without having to create a chart, which seems too time consuming. Thanks in advance for the help!


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.

fruit wrote:
Thanks for this method.
And what about the number 483?
We get three prime numbers 7, 23 and 3. What to do next?


\(483=3^1*7^1*23^1\) --> number of factors of 483 is: \((1+1)(1+1)(1+1)=8\).

For more on number properties see the Number Theory chapter of Math Book (link in my signature).

Hope it helps.
User avatar
fruit
Intern
Intern
Joined: 21 Feb 2010
Posts: 14
Own Kudos [?]: 14 [0]
Given Kudos: 9
Location: Ukraine
Send PM
Re: Finding Factors of Large Nums [#permalink] Finding Factors of Large Nums   10 Mar 2010, 10:07
I meant how to find all 8 factors? As you did in your example:


firasath wrote:
amenewyork wrote:

now work through the permutations of the exponents starting with 0:

2^0*7^0 = 1*1 = 1
2^0*7^1 = 1*7 = 7
2^0*7^2 = 1*49= 49

2^1*7^0 = 2*1=2
2^1*7^1 = 2*7=14
2^1*7^2 = 2*49 = 98

2^2*7^0 = 4*1=4
2^2*7^1 = 4*7=28
2^2*7^2 = 4*49 = 196

thus, the factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196


Does GMAT check this knowledge?
User avatar
firasath
Intern
Intern
Joined: 04 Feb 2007
Posts: 49
Own Kudos [?]: 180 [1]
Given Kudos: 16
Send PM
Re: Finding Factors of Large Nums [#permalink] Finding Factors of Large Nums   10 Mar 2010, 15:00
1
Kudos
fruit wrote:
I meant how to find all 8 factors? As you did in your example:


firasath wrote:
amenewyork wrote:

now work through the permutations of the exponents starting with 0:

2^0*7^0 = 1*1 = 1
2^0*7^1 = 1*7 = 7
2^0*7^2 = 1*49= 49

2^1*7^0 = 2*1=2
2^1*7^1 = 2*7=14
2^1*7^2 = 2*49 = 98

2^2*7^0 = 4*1=4
2^2*7^1 = 4*7=28
2^2*7^2 = 4*49 = 196

thus, the factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196


Does GMAT check this knowledge?



3^0*7^0*23^0 = 1
3^0*7^0*23^1 = 23

3^0*7^1*23^0 = 7
3^0*7^1*23^1 = 161

3^1*7^0*23^0 = 3
3^1*7^0*23^1 = 69

3^1*7^1*23^0 = 21
3^1*7^1*23^1 = 483

your factors are: 1,3,7,21,23,69,161,483
User avatar
Exellon
Intern
Intern
Joined: 14 Mar 2010
Posts: 36
Own Kudos [?]: 6 [0]
Given Kudos: 0
Send PM
Re: Finding Factors of Large Nums [#permalink] Finding Factors of Large Nums   15 Mar 2010, 15:12
How do you quickly determine a,b, c and p, q, r in the typical n=a^p*b^q*c^r formula?

Seems like guesswork to me...



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: Finding Factors of Large Nums [#permalink]
15 Mar 2010, 15:12
Moderator:
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts