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How many distinct positive factors does 30,030 have?

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How many distinct positive factors does 30,030 have? [#permalink]  18 Dec 2012, 03:07
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60% (02:30) correct 40% (01:25) wrong based on 91 sessions
How many distinct positive factors does 30,030 have?

A. 16
B. 32
C. 64
D. 128
E. 256
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Dec 2012, 03:26, edited 1 time in total.
Moved to PS forum and added OA.
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Re: How many distinct positive factors does 30,030 have? [#permalink]  18 Dec 2012, 03:30
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Expert's post
Drik wrote:
How many distinct positive factors does 30,030 have?

A. 16
B. 32
C. 64
D. 128
E. 256

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:

Factorize 30,030=2*3*5*7*11*13, thus the number of factors of 30,030 is (1+1)(1+1)(1+1)(1+1)(1+1)(1+1)=2^6=64.

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Re: How many distinct positive factors does 30,030 have? [#permalink]  08 Feb 2015, 18:27
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Re: How many distinct positive factors does 30,030 have?   [#permalink] 08 Feb 2015, 18:27
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