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# The positive integer 200 has how many factors?

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Intern
Joined: 24 Jul 2012
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The positive integer 200 has how many factors? [#permalink]

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17 Sep 2012, 06:24
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72% (00:30) correct 28% (00:39) wrong based on 209 sessions

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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, 07:01, 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, 07:00
Expert's post
4
This post was
BOOKMARKED
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.

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, 16:23
Hello from the GMAT Club BumpBot!

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

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

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

Kudos [?]: 20 [0], given: 113

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132595 [0], given: 12326

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

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21 Aug 2015, 08:32
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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Current Student
Joined: 20 Mar 2014
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Concentration: Finance, Strategy
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Re: The positive integer 200 has how many factors? [#permalink]

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21 Aug 2015, 08:33
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, 09:24
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.

Kudos [?]: 20 [0], given: 113

Current Student
Joined: 20 Mar 2014
Posts: 2676

Kudos [?]: 1767 [1], given: 794

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
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Re: The positive integer 200 has how many factors? [#permalink]

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21 Aug 2015, 09:41
1
KUDOS
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.

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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26 Aug 2016, 05:06
Hello from the GMAT Club BumpBot!

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

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14 Dec 2016, 08:45
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.

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?

Kudos [?]: 5 [0], given: 12

Math Expert
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Posts: 42249

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

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14 Dec 2016, 08:51
3
KUDOS
Expert's post
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.

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?

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, 08:56
Many many thanks for the lightning fast reply
You're the best

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Re: The positive integer 200 has how many factors?   [#permalink] 14 Dec 2016, 08:56
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