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

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Intern
Joined: 16 Apr 2017
Posts: 2
A is a prime number (A>2). If B = A^3, by how many different integers  [#permalink]

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Updated on: 27 Sep 2017, 21:08
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Difficulty:

35% (medium)

Question Stats:

60% (00:43) correct 40% (00:46) wrong based on 55 sessions

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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

Originally posted by Huey002 on 27 Sep 2017, 18:58.
Last edited by Bunuel on 27 Sep 2017, 21:08, edited 1 time in total.
Renamed the topic and edited the question.
Intern
Joined: 27 Nov 2016
Posts: 45
Location: India
Schools: ISB '19
GPA: 2.75
Re: A is a prime number (A>2). If B = A^3, by how many different integers  [#permalink]

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

+1 Kudos if it helped.
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Joined: 02 Sep 2009
Posts: 47200
A is a prime number (A>2). If B = A^3, by how many different integers  [#permalink]

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27 Sep 2017, 21:07
2
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 $$3+1=4$$: $$1$$, $$a$$, $$a^2$$, $$a^3=b$$.

P.S. PLEASE NAME TOPICS PROPERLY. CHECK RULE 3 HERE: RULES OF POSTING. Thank you.
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A is a prime number (A>2). If B = A^3, by how many different integers &nbs [#permalink] 27 Sep 2017, 21:07
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