Question

Consider the number $21600$. Find sum of the divisors.

Answer 1

Since $21600=6^3\cdot {10}^2=2^3.3^3.2^2.5^2=2^5.3^3.5^2$,
The number of divisors $=(5+1)(3+1)(2+1)=72$;
The sum of the divisors $=\frac{2^6-1}{2-1}\cdot \frac{3^4-1}{3-1}\cdot \frac{5^3-1}{5-1}$
$=63\times 40\times 31$
$=78120$.
Also $21600$ can be resolved into two factors prime to each other in $2^3-1$, or $4$ ways.