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 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.

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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