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# Number of distinct factors of a number

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Number of distinct factors of a number [#permalink]

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11 Sep 2012, 12:32
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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Re: Number of distinct factors of a number [#permalink]

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11 Sep 2012, 12:44
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.
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Re: Number of distinct factors of a number [#permalink]

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12 Sep 2012, 17:51
Factors are positive.

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Re: Number of distinct factors of a number [#permalink]

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12 Sep 2012, 20:34
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Expert's post
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.
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Re: Number of distinct factors of a number [#permalink]

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21 Sep 2012, 10:46
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?
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Re: Number of distinct factors of a number [#permalink]

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22 Sep 2012, 08:16
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
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Re: Number of distinct factors of a number [#permalink]

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09 Aug 2016, 00:19
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Number of distinct factors of a number   [#permalink] 09 Aug 2016, 00:19
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