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# Number of distinct factors of a number

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Intern
Joined: 22 Jan 2012
Posts: 2
Number of distinct factors of a number  [#permalink]

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11 Sep 2012, 11:32
1
Hi,

I have a doubt in questions where we are asked to find the number of distinct factors of a number.

Do we have to consider the total number of factors which are positive factors + negative factors or only the positive factors?

Example:
Q. Distinct prime factors of 36

Positive factors: 9
Negative factors: 9

So is the answer to the question be 9 or 18 ?

Can the factors be negative or they are always positive?
Manager
Joined: 02 Jun 2011
Posts: 56
Re: Number of distinct factors of a number  [#permalink]

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11 Sep 2012, 11:44
Kannagi wrote:
Hi,

I have a doubt in questions where we are asked to find the number of distinct factors of a number.

Do we have to consider the total number of factors which are positive factors + negative factors or only the positive factors?

Example:
Q. Distinct prime factors of 36

Positive factors: 9
Negative factors: 9

So is the answer to the question be 9 or 18 ?

Can the factors be negative or they are always positive?

When factors are asked it simply mean the positive factors only. and all should be integer. fractions, irrationals none are allowed.
Intern
Joined: 21 Jan 2012
Posts: 14
Re: Number of distinct factors of a number  [#permalink]

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12 Sep 2012, 16:51
Factors are positive.

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8795
Location: Pune, India
Re: Number of distinct factors of a number  [#permalink]

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12 Sep 2012, 19:34
1
Kannagi wrote:
Hi,

I have a doubt in questions where we are asked to find the number of distinct factors of a number.

Do we have to consider the total number of factors which are positive factors + negative factors or only the positive factors?

Example:
Q. Distinct prime factors of 36

Positive factors: 9
Negative factors: 9

So is the answer to the question be 9 or 18 ?

Can the factors be negative or they are always positive?

Factors are always positive.
No of distinct prime factors of 36 is 2 (they are 2 and 3)
No of distinct factors of 36 is 9.

Multiple can be positive/0/negative.
There are infinite multiples of any integer e.g. multiples of 36 are 36, 72, 0, -36, -72 etc.
0 is a multiple of every number.
_________________

Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 22 Jan 2012
Posts: 2
Re: Number of distinct factors of a number  [#permalink]

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21 Sep 2012, 09:46
Hi Karishma,

Please clarify the doubt stated below:

From the OG13:

If x and y are integers and x does not equal 0, then x is a divisor (factor) of y provided that y = xn for some integer n.

From this definition, we can see that -2 is a factor of 10, since we can express 10 as the product of -2 and some integer. That is 10 = (-2)(-5)

So, can negative numbers be factors?
Manager
Status: faciendo quod indiget fieri
Joined: 13 Mar 2012
Posts: 71
Re: Number of distinct factors of a number  [#permalink]

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22 Sep 2012, 07:16
Firstly, negative factors are possible! ans its very clear from the definition you provided.

BUT, and its a big BUT that we will NEVER use negative factors on the gmat.

It is also a topic of debate among some theorists, but on GMAT FACTORS ARE ALWAYS POSITIVE. Period

problem will MOSTLY have the words : positive factors to make it explicitly clear
Non-Human User
Joined: 09 Sep 2013
Posts: 9454
Re: Number of distinct factors of a number  [#permalink]

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06 Feb 2018, 20:04
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Re: Number of distinct factors of a number &nbs [#permalink] 06 Feb 2018, 20:04
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