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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.

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

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05 Dec 2014, 16:23

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

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26 Aug 2016, 05:06

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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.

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

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.

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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