[Pairings and groupings; bijections ] [ Products and factorials $\quad$]

A natural number $A$ has exactly 100 different divisors (including 1 and $A$). Find their product.
Each divisor $d$ of the number $A$ corresponds to another divisor $A / d$.

## Solution

Notice that if the number $d$ is a divisor of the number $A$, then the number $A / d$ is also a divisor of the number $A$. Since $A$ has 100 divisors, they are divided into 50 such pairs.

## Answer

$A^{50}$.