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divisors and factors

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25 Jun 2010, 13:58
Lets try to illustrate what I want to discuss with an example.

i) What is the sum of all common divisors of 48 and 36?

A)6
B)8
C)5
D)104
E)28

48=2.2.2.2.3
36=2.2.3.3

Common divisors={2,3}. Therefore 2+3=5, so it is C.
On the other hand, if the question were ii)What is the sum of all common factors of 48 and 36?

The common factor are 1,2,3,4,6,12. Their sum is 28, so it would be D.

Everybody agree? Well, Im afraid that what I have said above is not completely correct...
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25 Jun 2010, 14:02
I think the first question should be:

1. Sum of "Prime" factors of 48 and 36

And the second question should be: Sum of factors/divisors.
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25 Jun 2010, 14:09
whiplash2411 wrote:
I think the first question should be:

1. Sum of "Prime" factors of 48 and 36

And the second question should be: Sum of factors/divisors.

So you say the words factors and divisors are synonyms?
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25 Jun 2010, 14:18
Yeah, I think they are. Prime factors are different. A divisor is basically a number that can divide another number. For example:

36 = 6x6 = 9x4 = 12x3 = 18x2 = 36x1

So: 1,2,3,4,6,9,12,18 and 36 are factors or divisors.

However, $$36 = (2)^2 * (3)^2$$

So these are the only two prime factors. I might be wrong, but I think that's how it's done.
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26 Jun 2010, 03:25
As far as i know, factors and divisors are synonyms in GMAT.
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26 Jun 2010, 03:56
hardnstrong wrote:
As far as i know, factors and divisors are synonyms in GMAT.

OK, it´s good to know. That makes sense with some OA I have seen.

I have been using divisor all my life to refer to the "prime" factors, and factors to all the numbers by which you can divide a number. It´s time to change my mind for the GMAT.

Thanks!
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29 Jun 2010, 19:44
Hi,

All of the following are the SAME question:

Is x a multiple of y?
Is y a factor of x?
Is y a divisor of x?
Is x a dividend of y?
Is x divisible by y?
Does the quotient x/y yield an integer value?

"divisor" and "factor" are synonymous in math.
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30 Jun 2010, 05:26
The should definitely be common "prime" factors.
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06 Jan 2011, 01:50
Is there a systematic way to calculate the sum of all factors of a number?
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06 Jan 2011, 01:55
From the GMAT Club Math Book:

Finding the Sum of the 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 sum of factors of n will be expressed by the formula: $$\frac{(a^{p+1}-1)*(b^{q+1}-1)*(c^{r+1}-1)}{(a-1)*(b-1)*(c-1)}$$

Example: Finding the sum of all factors of 450:$$450=2^1*3^2*5^2$$

The sum of all factors of 450 is $$\frac{(2^{1+1}-1)*(3^{2+1}-1)*(5^{2+1}-1)}{(2-1)*(3-1)*(5-1)}=\frac{3*26*124}{1*2*4}=1209$$
Re: divisors and factors   [#permalink] 06 Jan 2011, 01:55
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