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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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17 Sep 2012, 05:24
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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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Re: The positive integer 200 has how many factors? [#permalink]

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17 Sep 2012, 06:00
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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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05 Dec 2014, 15:23
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The positive number 200 has how many factors? [#permalink]

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

A: 2
B: 10
C: 12
D: 15
E: 24
Math Expert
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Re: The positive integer 200 has how many factors? [#permalink]

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21 Aug 2015, 07:32
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.
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Re: The positive integer 200 has how many factors? [#permalink]

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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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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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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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GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
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Re: The positive integer 200 has how many factors? [#permalink]

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

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14 Dec 2016, 07:45
Bunuel wrote:
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.

Hi Bunuel
As of 2016 do we consider negative factors also in the GMAT ,
as in factors of 200=(2)^3*(5)^2-->(3+1)(2+1)positive factors-->2*12(both positive and negative factors)=24?
I appreciate your input
Thanks in advance
Math Expert
Joined: 02 Sep 2009
Posts: 36583
Followers: 7087

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

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14 Dec 2016, 07:51
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karanchamp1 wrote:
Bunuel wrote:
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.

Hi Bunuel
As of 2016 do we consider negative factors also in the GMAT ,
as in factors of 200=(2)^3*(5)^2-->(3+1)(2+1)positive factors-->2*12(both positive and negative factors)=24?
I appreciate your input
Thanks in advance

No. A factor is a positive divisor.
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Re: The positive integer 200 has how many factors? [#permalink]

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14 Dec 2016, 07:56
Many many thanks for the lightning fast reply
You're the best
Re: The positive integer 200 has how many factors?   [#permalink] 14 Dec 2016, 07:56
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