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

It is currently 31 Aug 2015, 17:59
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the sum of all the factors of 12972960

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
SVP
SVP
User avatar
Joined: 05 Jul 2006
Posts: 1516
Followers: 5

Kudos [?]: 142 [0], given: 39

GMAT ToolKit User
What is the sum of all the factors of 12972960 [#permalink] New post 12 Sep 2006, 11:16
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

What is the sum of all the factors of 12972960?
SVP
SVP
User avatar
Joined: 05 Jul 2006
Posts: 1516
Followers: 5

Kudos [?]: 142 [0], given: 39

GMAT ToolKit User
 [#permalink] New post 12 Sep 2006, 13:13
anyone..... it is a good to know??
VP
VP
User avatar
Joined: 02 Jun 2006
Posts: 1266
Followers: 2

Kudos [?]: 52 [0], given: 0

 [#permalink] New post 12 Sep 2006, 14:07
Yezz,
Based on your problem I went out researching and found some interesting things. Suffice to say I second your statement about this being useful...

Ok.. given any number n we define the following functions:

a. D(n) := the total number of +ve divisors of n

b. σk(n) := the divisor function, which is the sum of the k-th powers of all the positive divisors of n

Specifically by definition :
* σ0(n) = d(n) (k = 0)
* σ1(n) = σ(n), (k = 1)

Both these functions are multiplicative i.e.

D(a x b) = D(a) x D(b) &
σk(a x b) = σk(a) x σk(b)

For example:
144 = 12 x 12
= 2x2x3 x 2x2x3
= 2^4 x 3^2

Therefore D(n) = # of +ve divisors of 144
= D(144) = σ0(2^4 x 3^2)
= σ0(2^4) x σ0(3^2)
= (1^0 + 2^0+4^0+8^0+16^0) x (1^0 + 3^0 +9^0)
= 5 x 3
= 15

Therefore total number of divisors of 144 = 15.

Similarly sum of all the divisors of 144 = σ1(144)
= σ1(2^4 x 3^2)
= σ1(2^4) x σ1(3^2)
= (1^1 + 2^1+4^1+8^1+16^1) x (1^1 + 3^1 + 9^1)
= 31 x 13 = 403

For the given problem the number 1297296 = 2^4 x 3^4 x 7 x 11 x 13

Therefore sum of divisors = σ1(2^4 x 3^4 x 7x11x13)
= σ1(2^4) x σ1(3^4) x σ1(7) x σ1(11)xσ1(13)
= (1^1+2^1+4^1+8+1+16^1) x (1^1+3^1+9^1+27^1+81^1)
x (1^1+7^1) x (1^1 +11^1)x(1^1+13^1)
= 31 x 121 x 8x 12x14
= 5041344

FYI the number of divisors of 1297296 = σ0(2^4 x 3^4 x 7x11x13) = 5 x 5 x 2 x 2 x 2= 200.

FYI: http://en.wikipedia.org/wiki/Multiplicative_function
SVP
SVP
User avatar
Joined: 05 Jul 2006
Posts: 1516
Followers: 5

Kudos [?]: 142 [0], given: 39

GMAT ToolKit User
 [#permalink] New post 13 Sep 2006, 01:14
Hi Haas thanks a lot for the support and effort you did.

My aim is to show a very new concept ( at least to myself) to calculate the sum of all the factors of a certain intiger as above.

1) Find all the prime factors for this intiger

say it is (a^x*b^y*c*z...etc)

the sum of all the factors can be calculated through this formula

(a^(x+1) - 1)/(a-1) * (b^(y+1) - 1)/(b-1) * (c^(z+1) - 1)/(c-1)

2) to find the total count (number of factors ) of any intiger including (1, the intiger itself) can be calcultated through the following formula

(x+1) * (y+1) * (z+1)

Hope this helps
  [#permalink] 13 Sep 2006, 01:14
Display posts from previous: Sort by

What is the sum of all the factors of 12972960

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.