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If n is an integer, then n is divisible by how many positive [#permalink]
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11 Jun 2008, 23:47
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If n is an integer, then n is 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. OPEN DISCUSSION OF THIS QUESTION IS HERE: ifnisanintegerthennisdivisiblebyhowmanypositive164964.htmlOA: D
ii) i understand
but if i)
let prime numbers be 3,4, then there are 4 possible divisors (1,3,4,12) but if the prime numbers are 1,2, then there are only 2 possible divisors (1,2)
anyone?
nm just realized that 1 is not a prime number.
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Last edited by Bunuel on 08 Feb 2014, 02:05, edited 1 time in total.
Renamed the topic, edited the question and added the OA.



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Re: DS Q [#permalink]
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12 Jun 2008, 00:02
zetaexmachina wrote: let prime numbers be 3,4, then there are 4 possible divisors (1,3,4,12) but if the prime numbers are 1,2, then there are only 2 possible divisors (1,2)
anyone?
nm just realized that 1 is not a prime number. 4 and 1 are not prime numbers. 3,5  (1,3,5,15) 5,7  (1,5,7,35)
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Re: If n is an integer, n is divisible by how many positive [#permalink]
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07 Feb 2014, 18:37
If n is an integer, n is divisible by how many positive integers? > # factors of n????
i) n is the product of two prime numbers > n = p^1 * q^1, where p and q are prime; number of factors of n = 4. ii) n and 2^3 are each divisible by the same number of positive integers > 2^3 has 4 factors => n has 4 factors.
D



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Re: If n is an integer, then n is divisible by how many positive [#permalink]
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08 Feb 2014, 02:05
Finding the Number of Factors of an IntegerFirst 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: mathnumbertheory88376.htmlBACK TO THE ORIGINAL QUESTION: If n is an integer, then n is 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. Answer: D. OPEN DISCUSSION OF THIS QUESTION IS HERE: ifnisanintegerthennisdivisiblebyhowmanypositive164964.html
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Re: If n is an integer, then n is divisible by how many positive
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