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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]  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]  17 Sep 2012, 06:00
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Expert's post
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]  05 Dec 2014, 15:23
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Re: The positive integer 200 has how many factors?   [#permalink] 05 Dec 2014, 15:23
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