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# The number 10010 has how many positive integer factors?

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Intern
Joined: 24 Jul 2017
Posts: 6
The number 10010 has how many positive integer factors?  [#permalink]

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Updated on: 11 Feb 2018, 00:04
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Difficulty:

15% (low)

Question Stats:

82% (01:52) correct 18% (01:56) wrong based on 43 sessions

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The number 10010 has how many positive integer factors?

A. 30
B. 32
C. 34
D. 36
E. 38

Originally posted by sxsd on 10 Feb 2018, 23:59.
Last edited by Bunuel on 11 Feb 2018, 00:04, edited 1 time in total.
Renamed the topic.
Math Expert
Joined: 02 Sep 2009
Posts: 50623
Re: The number 10010 has how many positive integer factors?  [#permalink]

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11 Feb 2018, 00:06
sxsd wrote:
The number 10010 has how many positive integer factors?

A. 30
B. 32
C. 34
D. 36
E. 38

Factorize: 10010 = 2*5*7*11*13.

Number of factors = (1 + 1)(1 + 1)(1 + 1)(1 + 1) = 32.

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.
_________________
Re: The number 10010 has how many positive integer factors? &nbs [#permalink] 11 Feb 2018, 00:06
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