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A is a prime number (A>2). If B = A^3, by how many different integers

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A is a prime number (A>2). If B = A^3, by how many different integers [#permalink]

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New post 27 Sep 2017, 18:58
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A is a prime number (A>2). If B = A^3, by how many different integers can B be equally divided?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Sep 2017, 21:08, edited 1 time in total.
Renamed the topic and edited the question.

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Re: A is a prime number (A>2). If B = A^3, by how many different integers [#permalink]

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New post 27 Sep 2017, 19:04
Easy
Take 3
3^3 has 4 factors. Hence B

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A is a prime number (A>2). If B = A^3, by how many different integers [#permalink]

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New post 27 Sep 2017, 21:07
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Huey002 wrote:
A is a prime number (A>2). If B = A^3, by how many different integers can B be equally divided?

(a) 3.
(b) 4.
(c) 5.
(d) 6.
(e) 7.


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.

According to above as \(b=a^3\) and \(a\) is a prime, then the number of factors of \(b\) is \(3+1=4\): \(1\), \(a\), \(a^2\), \(a^3=b\).

Answer: B.

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A is a prime number (A>2). If B = A^3, by how many different integers   [#permalink] 27 Sep 2017, 21:07
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