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# Number of factors

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Intern
Joined: 04 Oct 2015
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14 Oct 2015, 05:29
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Number of factors of A = 2^3 * 5^7 * 7^2

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Joined: 02 Sep 2009
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14 Oct 2015, 10:19
Sujan Sareen wrote:
Number of factors of A = 2^3 * 5^7 * 7^2

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.

Check for more here: math-number-theory-88376.html

So, the number of factors of $$2^3 * 5^7 * 7^2$$ is $$(3 + 1)(7 + 1)(2 + 1) = 96$$.
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23 Oct 2015, 12:04
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We have a free video that explains the rule that Bunuel used - http://www.gmatprepnow.com/module/gmat- ... /video/828

Cheers,
Brent
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29 Oct 2015, 16:52
I'm curious why you say that 192 is the real answer. Do you have a copy of the full question? (If that's all there is, then it's simply an error. Bunuel, of course, is correct.)
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28 Jan 2018, 23:51
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Number of factors &nbs [#permalink] 28 Jan 2018, 23:51
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