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

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

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19 Feb 2011, 10:29
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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.

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Joined: 02 Sep 2009
Posts: 57244

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19 Feb 2011, 10:40
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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, 22:52
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.

Please provide detailed explanations. Thanks!
Intern
Joined: 27 Dec 2012
Posts: 11

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30 Jan 2013, 22:33
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, 13:10
@ 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, 01:45
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

Don't have OA. Please provide explanations! Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 57244
Re: if n is an integer then n is divisble by how many positive i  [#permalink]

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17 Jul 2013, 01:50
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

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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Re: If n is an integer, then n divisible by how many positive  [#permalink]

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14 Aug 2018, 05:24
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Re: If n is an integer, then n divisible by how many positive   [#permalink] 14 Aug 2018, 05:24
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