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Question Regarding Multiples, factors and primes!

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Question Regarding Multiples, factors and primes! [#permalink] New post 09 Nov 2011, 15:11
I have a few questions regarding multiples, factors and primes and I would really appreciate an input.

1. When a GMAT question asks you to find the total number of factors, should we include the negative factors as well? I read a Gmat book where it defines factors as positive numbers.. could someone elaborate on that a bit more please? The factors of 4 are 2 or 4? When the GMAT says factor should we assume that it means only positive ones, or we should not assume anything?

2. Also, when a GMAT question says that a number has 2 factors: Then someone could assume that it is a prime number. But if we define factors as negative numbers too, the only number with 2 factors would be 1. (Does it have to say only 2 factors to mean 2 numbers? or if it says 2 factors we could assume that there could be more?)

3. When a GMAT question says that a is divisible by b. Someone could say that a >= b. I would argue that -3 could be divisible by 1 therefore the aforementioned doesn't apply.

4. Also, when it talks about multiples of a number, should we include negative ones and 0 as well? Could we talk about multiples of a decimal number? or only of integers?

5. Can factors be decimal numbers? for example. 16 is divisible by 0,2 since the result is an integer. Can we say that 0,2 is a factor of 16?

6. If a questions says that n is divisible by 3. Can we say that n must be an integer because the product of 2 integers can only be an integer. Meaning, n=3*k, since k is integer, n must also be integer. Is the aforementioned logic correct?

7. If we know that a divides b. Can a and b be decimals? If they can be decimals, then b has infinite factors. for example if b is 0,3 then a could be 3/10, 3/20, 3/30 etc... Therefore a decimal has infinite number of factors? Could we assume that if it says that a number has a finite number of factors, that this number cannot be decimal? Therefore if it states that a number has only 2 positive factors, we can assume this is an integer (prime number) and not a decimal (since it has a finite number of factors?)

I have asked the question around without a decent answer yet... I would really appreciate a decent answer...btw sorry for the huge post!
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Re: Question Regarding Multiples, factors and primes! [#permalink] New post 14 Nov 2011, 09:53
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SonyGmat wrote:
VeritasPrepKarishma wrote:

Thank you so much Karishma!!! +1 great link... was very helpful!

So every time we see factor we know it means positive factor! Correct?

One more question though, if a Question say that X is a multiple of Y:
According to the multiple definition you gave me( "Multiples are numbers which we get by multiplying an integer by another integer"). Thus, X can be negative.

But we know that X is a multiple of Y is equivalent to X is divisible by Y but based to you post, divisibility is applied to positive numbers only so X must be positive... Thus, X can't be negative.

I think that the statements contradict each other..


Actually, no. More often that not, we use just the positive multiples and that is when we say X is a multiple of Y implies X is divisible by Y. In divisibility questions, you will see that they mention 'x and y are positive integers', 'n is a positive integer' etc. The reason is that a divisible by b makes sense only when both are positive integers (as explained in the link given above). If we are talking about negative multiples, 'X is divisible by Y' is not logical.
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Re: Question Regarding Multiples, factors and primes! [#permalink] New post 09 Nov 2011, 18:24
I guess a few points will answer all your questions.

Factors:
- Positive Integers
- No decimal part

Multiples
- GMAT doesnt test negative multiples directly.

And whenever GMAT uses them it does mention things that closes us all the doubts. In q6. U asked n divisible by 3. Here the gmat will mention n is an integer.
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Re: Question Regarding Multiples, factors and primes! [#permalink] New post 11 Nov 2011, 03:06
VeritasPrepKarishma wrote:

Thank you so much Karishma!!! +1 great link... was very helpful!

So every time we see factor we know it means positive factor! Correct?

One more question though, if a Question say that X is a multiple of Y:
According to the multiple definition you gave me( "Multiples are numbers which we get by multiplying an integer by another integer"). Thus, X can be negative.

But we know that X is a multiple of Y is equivalent to X is divisible by Y but based to you post, divisibility is applied to positive numbers only so X must be positive... Thus, X can't be negative.

I think that the statements contradict each other..
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Re: Question Regarding Multiples, factors and primes! [#permalink] New post 14 Nov 2011, 15:18
VeritasPrepKarishma wrote:
Actually, no. More often that not, we use just the positive multiples and that is when we say X is a multiple of Y implies X is divisible by Y. In divisibility questions, you will see that they mention 'x and y are positive integers', 'n is a positive integer' etc. The reason is that a divisible by b makes sense only when both are positive integers (as explained in the link given above). If we are talking about negative multiples, 'X is divisible by Y' is not logical.


Okey! Thanks a lot!
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Re: Question Regarding Multiples, factors and primes! [#permalink] New post 02 Jul 2014, 01:01
Hi Karishma,
Could you please repost the link. It seems that it has been deleted, as I am not able to find it, or could you please answer all the questions raised by sonygmat.
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Re: Question Regarding Multiples, factors and primes! [#permalink] New post 02 Jul 2014, 21:18
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tiwariayush03 wrote:
Hi Karishma,
Could you please repost the link. It seems that it has been deleted, as I am not able to find it, or could you please answer all the questions raised by sonygmat.


Here goes:
http://www.veritasprep.com/blog/2010/12 ... ly-number/
http://www.veritasprep.com/blog/2010/12 ... t-squares/
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Re: Question Regarding Multiples, factors and primes!   [#permalink] 02 Jul 2014, 21:18
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