If n is an integer, then n divisible by how many positive : GMAT Data Sufficiency (DS)
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# If n is an integer, then n divisible by how many positive

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19 Feb 2011, 09:29
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If n is an integer, then n divisible by how many positive integers?

(1) n is the product of two different prime numbers.
(2) n and 2^3 are each divisible by the same number of positive integers.
[Reveal] Spoiler: OA

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19 Feb 2011, 09:40
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Baten80 wrote:
If n is an integer, then n divisible by how many positive integers?
(1) n is the product of two different prime numbers.
(2) n and 2^3 are each divisible by the same number of positive integers.

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.
For more on number properties check: math-number-theory-88376.html

BACK TO THE ORIGINAL QUESTION:

If n is an integer, then n divisible by how many positive integers?

(1) n is the product of two different prime numbers --> n=ab, where a and b are primes, so # of factors is (1+1)(1+1)=4. Sufficient.

(2) n and 2^3 are each divisible by the same number of positive integers --> 2^3 has 4 different positive factors (1, 2, 4, and 8) so n has also 4. Sufficient.

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if n is an integer, then n is divisible by how many positive [#permalink]

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29 Jan 2013, 21:52
if n is an integer, then n is divisible by how many positive integers?

1) n is the product of two different integers
2) n and 2^3 are each divisible by the same number of positive integers.

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30 Jan 2013, 21:33
It took me just 15 seconds to solve this..
N is a product of 2 different prime nos.......then 1,n and dose two prime nos. are divisible by n ...hence 4 nos.
agen, 2^3 = 8, has 4 nos. from which it can be divided...agen n is divisible by 4 nos.
Hence, D
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Re: If n is an integer, then n divisible by how many positive [#permalink]

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31 Jan 2013, 12:10
@ Fozzzy
Statement 1 - n is the product of two different integers . They may be 2*3 or 3*7 or any two integers. Since they yield different products. We cannot determine the # of factors for n. Hence Statement 1 - Insufficient.
Statement 2 - n and 2^3 are each divisible by the same number of positive integers. 2^3 = 8. Having 4 factors (1,2,4,8) . Since the statement says n and 8 are divisible by the same num of integers. n=4. Hence Statement 2 - Sufficient

Hope this helps!
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if n is an integer then n is divisble by how many positive i [#permalink]

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17 Jul 2013, 00:45
if n is an integer then n is divisble by how many positive integers?

1) n is the product of two different prime numbers.
2) n and $$2^ {-3}$$ are each divisible by the same number of positive integers

[Reveal] Spoiler:
Don't have OA. Please provide explanations! Thanks

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Re: if n is an integer then n is divisble by how many positive i [#permalink]

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17 Jul 2013, 00:50
fozzzy wrote:
if n is an integer then n is divisble by how many positive integers?

1) n is the product of two different prime numbers.
2) n and $$2^ {-3}$$ are each divisible by the same number of positive integers

[Reveal] Spoiler:
Don't have OA. Please provide explanations! Thanks

Merging similar topics. Please refer to the solution above and ask if anything remains unclear.

P.S. You've posted this question before: if-n-is-an-integer-then-n-divisible-by-how-many-positive-109670.html#p1175381
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26 Aug 2014, 19:29
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Re: If n is an integer, then n divisible by how many positive [#permalink]

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14 Sep 2016, 04:50
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Re: If n is an integer, then n divisible by how many positive   [#permalink] 14 Sep 2016, 04:50
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