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B
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Difficulty:
25%
(medium)
Question Stats:
71% (00:55) correct
29%
(01:21)
wrong
based on 122
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If A is a prime number and B = A^3, by how many different positive integers is B divisible?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
A is a prime number (A>2). If B = A^3, by how many different integers can B be equally divided?
27 Sep 2017, 21:07
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Huey002
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.
P.S. PLEASE NAME TOPICS PROPERLY. CHECK RULE 3 HERE: RULES OF POSTING. Thank you.
15 Sep 2024, 00:00
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Bunuel, the question asks "by how many different integers can B be equally divided?"
What is the relevance of equally divided ? That phrase completely threw me off. I understand that the number has 4 factors, 1, a, a^2, a^3.
Is the language of this question something we can expect in an official test ?
What is the relevance of equally divided ? That phrase completely threw me off. I understand that the number has 4 factors, 1, a, a^2, a^3.
Is the language of this question something we can expect in an official test ?
