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# The positive integer 200 has how many factors?

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Intern
Joined: 24 Jul 2012
Posts: 13
Schools: Schulich '16
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The positive integer 200 has how many factors? [#permalink]

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Updated on: 17 Sep 2012, 07:01
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Question Stats:

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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

Originally posted by Vamshi8411 on 17 Sep 2012, 06:24.
Last edited by Bunuel on 17 Sep 2012, 07:01, edited 2 times in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 44655
Re: The positive integer 200 has how many factors? [#permalink]

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17 Sep 2012, 07:00
1
KUDOS
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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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.

Current Student
Joined: 20 Mar 2014
Posts: 2645
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
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.
Intern
Joined: 27 Aug 2016
Posts: 25
Location: India
Concentration: Entrepreneurship, Marketing
GPA: 3.87
WE: Sales (Internet and New Media)
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?
Math Expert
Joined: 02 Sep 2009
Posts: 44655
Re: The positive integer 200 has how many factors? [#permalink]

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14 Dec 2016, 08:51
4
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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Location: India
Concentration: Entrepreneurship, Marketing
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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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Joined: 12 Sep 2015
Posts: 2325
Re: The positive integer 200 has how many factors? [#permalink]

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26 Nov 2017, 12:24
1
KUDOS
Expert's post
Top Contributor
Vamshi8411 wrote:
The positive integer 200 has how many factors?

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

APPROACH #1 - FORMULA
If the prime factorization of N = (p^a)(q^b)(r^c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (a+1)(b+1)(c+1)(etc) positive divisors.

Example: 14000 = (2^4)(5^3)(7^1)
So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) =(5)(4)(2) = 40

Now onto the question...
Example: 200 = (2^3)(5^2)
So, the number of positive divisors of 200 = (3+1)(2+1)
= (4)(3)
= 12
= C

APPROACH #2 - LIST
We can quickly list all of the factors of 200
I suggest we do so in PAIRS of values whose product is 200
We get:
1 and 200
2 and 100
4 and 50
5 and 40
8 and 25
10 and 20
DONE!

Total = 12
= C

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

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29 Nov 2017, 11:15
Vamshi8411 wrote:
The positive integer 200 has how many factors?

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

We can break 200 into primes, then add 1 to each exponent and find the product of all the sums. That product will give us the number of total factors.

200 = 20 x 10 = 2^2 x 5^1 x 2^1 x 5^1 = 2^3 x 5^2

Thus, 200 has (3 + 1)(2 + 1) = 4 x 3 = 12 factors.

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Re: The positive integer 200 has how many factors?   [#permalink] 29 Nov 2017, 11:15
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