isi-entrance 2023 Q15

isi-entrance · India · UGA Number Theory Divisibility and Divisor Analysis

Let $n$ be a positive integer having 27 divisors including 1 and $n$, which are denoted by $d _ { 1 } , \ldots , d _ { 27 }$. Then the product of $d _ { 1 } , d _ { 2 } , \ldots , d _ { 27 }$ equals
(A) $n ^ { 13 }$.
(B) $n ^ { 14 }$.
(C) $n ^ { \frac { 27 } { 2 } }$.
(D) $27 n$.

Let $n$ be a positive integer having 27 divisors including 1 and $n$, which are denoted by $d _ { 1 } , \ldots , d _ { 27 }$. Then the product of $d _ { 1 } , d _ { 2 } , \ldots , d _ { 27 }$ equals\\
(A) $n ^ { 13 }$.\\
(B) $n ^ { 14 }$.\\
(C) $n ^ { \frac { 27 } { 2 } }$.\\
(D) $27 n$.

Paper Questions

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