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The positive integer 200 has how many factors?

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The positive integer 200 has how many factors? [#permalink]

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The positive integer 200 has how many factors?

A. 2
B. 10
C. 12
D. 15
E. 24

Can someone help me with a formula for such type of questions?
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Sep 2012, 06:01, edited 2 times in total.
Edited the question.
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Vamshi8411 wrote:
The positive integer 200 has how many factors?

A. 2
B. 10
C. 12
D. 15
E. 24

Can someone help me with a formula for such type of questions?


Finding the Number of 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 number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.

BACK OT THE ORIGINAL QUESTION:

\(200=2^3*5^2\), so it has (3+1)(2+1)=12 different factors.

Answer: C.

For more check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.
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Re: The positive integer 200 has how many factors? [#permalink]

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The positive number 200 has how many factors? [#permalink]

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New post 21 Aug 2015, 06:33
The positive number 200 has how many factors?

A: 2
B: 10
C: 12
D: 15
E: 24
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New post 21 Aug 2015, 07:32
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Re: The positive integer 200 has how many factors? [#permalink]

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New post 21 Aug 2015, 07:33
kamathimanshu wrote:
The positive number 200 has how many factors?

A: 2
B: 10
C: 12
D: 15
E: 24


The OA can not be E . It should be C

Direct formula for number of factors of a number N = a^p*b^q... = (p+1)(q+1)... And these include 1 and N as well.

Thus for 200= 2^3*5^2 -----> 4*3=12
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Re: The positive integer 200 has how many factors? [#permalink]

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New post 21 Aug 2015, 08:24
Bunuel wrote:
kamathimanshu wrote:
The positive number 200 has how many factors?

A: 2
B: 10
C: 12
D: 15
E: 24


Merging topics.

Please refer to the discussion above.



Can negative numbers also be factors.
If so the answer turns out to be 12*2 = 24.

Please help?
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Re: The positive integer 200 has how many factors? [#permalink]

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New post 21 Aug 2015, 08:41
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kamathimanshu wrote:
Bunuel wrote:
kamathimanshu wrote:
The positive number 200 has how many factors?

A: 2
B: 10
C: 12
D: 15
E: 24


Merging topics.

Please refer to the discussion above.



Can negative numbers also be factors.
If so the answer turns out to be 12*2 = 24.


Please help?


As far as I have seen , "factors" in GMAT refers to positive factors only.
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Re: The positive integer 200 has how many factors? [#permalink]

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New post 26 Aug 2016, 04:06
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Re: The positive integer 200 has how many factors?   [#permalink] 26 Aug 2016, 04:06
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