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What is the sum of the factors of 8192? A 16380 B 16383 C

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What is the sum of the factors of 8192? A 16380 B 16383 C [#permalink] New post   15 Sep 2006, 03:53
What is the sum of the factors of 8192?

A 16380
B 16383
C 16386
D 16389
E 16391



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Re: What is the sum of the factors of 8192? A 16380 B 16383 C [#permalink] New post   15 Sep 2006, 05:34
What is the sum of the factors of 8192?

A 16380
B 16383
C 16386
D 16389
E 16391


factorizing 8192 = 2^13

sum of factors = (2^14 - 1 ) / (2-1) = 16383
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Re: What is the sum of the factors of 8192? A 16380 B 16383 C [#permalink] New post   Updated on: 15 Sep 2006, 08:36
B 16383

Factoring 8192 = 2^13

Factors of 8192 = 1,2,4,8,16.... 8192 (all powers of 2)


As this is a GP with r = 2 , n = 14 (including 1)

Sum = 1 x (2^14 - 1)/(2-1) = 8192 x 2 -1 = 16383

Originally posted by haas_mba07 on 15 Sep 2006, 05:59.
Last edited by haas_mba07 on 15 Sep 2006, 08:36, edited 1 time in total.
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Re: What is the sum of the factors of 8192? A 16380 B 16383 C [#permalink] New post   15 Sep 2006, 18:39
haas_mba07 wrote:
B 16383

Factoring 8192 = 2^13

Factors of 8192 = 1,2,4,8,16.... 8192 (all powers of 2)


As this is a GP with r = 2 , n = 14 (including 1)

Sum = 1 x (2^14 - 1)/(2-1) = 8192 x 2 -1 = 16383


Haas can you give a little bit more explaination?

What is GP?? how did you get that formula for SUM? Is it a common formula. I'd like to know how you got the numerator part and the denominator. I'm a little weak with this.
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Re: What is the sum of the factors of 8192? A 16380 B 16383 C [#permalink] New post   15 Sep 2006, 19:16
Sure... GP is Geometric progression...

Its a sequence of the type:

a, ar, ar^2, ar^3, .... ar^n

where each term is multiplied by a common factor r.

The Sum of such a series is given by:

Sn = a1 x (r^n -1)/(r-1)

where
a1 = first term
n = number of terms
r = common multiple

The formula is a common one.. search on google for "geometric progression" and you should get a lot of results.

uvs_mba wrote:
haas_mba07 wrote:
B 16383

Factoring 8192 = 2^13

Factors of 8192 = 1,2,4,8,16.... 8192 (all powers of 2)


As this is a GP with r = 2 , n = 14 (including 1)

Sum = 1 x (2^14 - 1)/(2-1) = 8192 x 2 -1 = 16383


Haas can you give a little bit more explaination?

What is GP?? how did you get that formula for SUM? Is it a common formula. I'd like to know how you got the numerator part and the denominator. I'm a little weak with this.
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Re: What is the sum of the factors of 8192? A 16380 B 16383 C [#permalink] New post   Updated on: 25 Sep 2008, 01:10
Folks, I'll give u a generalised formula to calculate the sum of the factors of any number.

First split the number into it's prime factors say

N = P1^a1 x P2^a2 x P3^a3 x............xPn^an

Sum of the factors:
[(P1^a1+1)-1]/P1-1 x [(P2^a2+1)-1]/P2-1 x ...........x[(Pn^an+1)-1]/Pn-1

Let's look at an example
127008 = 32 x 81 x 49 = 2^5 x 3^4 x 7^2

Sum of the factors is (2^6)-1/1 x (3^5)-1/2 x (7^3)-1/6
= 63 x 121 x 57 = 434511

I think it's clear
Regards,

Originally posted by cicerone on 16 Sep 2006, 02:17.
Last edited by cicerone on 25 Sep 2008, 01:10, edited 1 time in total.
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Re: What is the sum of the factors of 8192? A 16380 B 16383 C [#permalink] New post   16 Sep 2006, 02:27
cicerone , thanks for ur great help with those formulas

and the remainder problems too :wink:

those methods and help is what we all need on this forum.
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Re: What is the sum of the factors of 8192? A 16380 B 16383 C [#permalink] New post   16 Sep 2006, 02:35
yezz wrote:
cicerone , thanks for ur great help with those formulas

and the remainder problems too :wink:

those methods and help is what we all need on this forum.


Dear yezz,
I am member of many forums like these and I also work for one of the premier institutes in India which train students for CAT (one of the asia's toughest entrance for MBA admissions)and GMAT

I'll definitely help the students in this forum, by the way even i am planning to write GMAT in the next year. So i hope my services will continue in this forum bcause l am expecting to learn a lot of English from this forum

Regards,
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Re: What is the sum of the factors of 8192? A 16380 B 16383 C [#permalink] New post   16 Sep 2006, 02:52
Cicerone, great to have you with us :-D
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Re: What is the sum of the factors of 8192? A 16380 B 16383 C [#permalink] New post   16 Sep 2006, 07:57
Welcome to the club cicerone...

I am sure you will be helping a lot of people and hopefully learning something from them on the club too... the people on this board are always open to discussion and interaction... any time of the day 24x7. So you will always find someone on to answer any verbal questions you might have.


cicerone wrote:
Dear yezz,
I am member of many forums like these and I also work for one of the premier institutes in India which train students for CAT (one of the asia's toughest entrance for MBA admissions)and GMAT

I'll definitely help the students in this forum, by the way even i am planning to write GMAT in the next year. So i hope my services will continue in this forum bcause l am expecting to learn a lot of English from this forum

Regards,




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Re: What is the sum of the factors of 8192? A 16380 B 16383 C [#permalink]
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