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Kannagi
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Number of distinct factors of a number 11 Sep 2012, 12:32
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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?

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Number of distinct factors of a number 11 Sep 2012, 12:44
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Kannagi
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?
Show more

When factors are asked it simply mean the positive factors only. and all should be integer. fractions, irrationals none are allowed.
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Number of distinct factors of a number 12 Sep 2012, 17:51
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Factors are positive.
:)
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KarishmaB
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Number of distinct factors of a number 12 Sep 2012, 20:34
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Kannagi
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?
Show more

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.
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Number of distinct factors of a number 21 Sep 2012, 10:46
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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?
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Number of distinct factors of a number 22 Sep 2012, 08:16
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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
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Number of distinct factors of a number 02 Sep 2021, 13:19
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VeritasKarishma


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.
Show more

Dear VeritasKarishma, -2*-1 = 2. So -2 is a negative divisor. We have learnt in school that product of two negatives makes a positive. So is it that for the limited purpose of GMAT, negative factors are ignored? What might be the ideology behind the same?

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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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