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The positive integer 200 has how many factors?

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Vamshi8411
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The positive integer 200 has how many factors? [#permalink] New post   Updated on: 17 Sep 2012, 07:01
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A
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E

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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?
ShowHide Answer
Official Answer
C

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.
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Bunuel
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Re: The positive integer 200 has how many factors? [#permalink] New post   17 Sep 2012, 07:00
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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] New post   14 Dec 2016, 08:51
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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 :-D
Thanks in advance :-D


No. A factor is a positive divisor.
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Re: The positive integer 200 has how many factors? [#permalink] New post   21 Aug 2015, 08:33
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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] New post   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.

Please help?
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Re: The positive integer 200 has how many factors? [#permalink] New post   21 Aug 2015, 09:41
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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] New post   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.

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 :-D
Thanks in advance :-D
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Re: The positive integer 200 has how many factors? [#permalink] New post   14 Dec 2016, 08:56
Many many thanks for the lightning fast reply :-D
You're the best :-D
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Re: The positive integer 200 has how many factors? [#permalink] New post   26 Nov 2017, 12:24
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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] New post   29 Nov 2017, 11:15
Expert Reply
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.

Answer: C
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Re: The positive integer 200 has how many factors? [#permalink] New post   02 Sep 2021, 13:17
Dear Bunuel, -2*-1 = 2. So -2 is a negative divisor. We have learnt in school that product of two negatives makes a positive. So is it that for the limited purpose of GMAT, negative factors are ignored? What might be the ideology behind the same
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Re: The positive integer 200 has how many factors? [#permalink] New post   08 Aug 2023, 07:18
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Re: The positive integer 200 has how many factors? [#permalink]
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