<s>[INST] Finding the divisors of the number $p^3q^6$ My text says that $p^3q^6$ has 28 divisors. Could anyone please explain to me how they got 28 here?
Edit:
$p$ and $q$ are distinct prime numbers Sorry for the late addition..
 [/INST] Let's take $p=3$ and $q=2$ as an example.  Then the number is $3^32^6 = 1728$, and the 28 divisors of 1728 are:
$$\begin{matrix}
1&2&4&8&16&32&64 \\
3&6&12&24&48&96&192 \\
9 & 18 & 36 & 72 & 144 & 288 & 576 \\
27 & 54 & 108 & 216 & 432 & 864 & 1728 
\end{matrix}$$
These values are, respectively:
$$\begin{matrix}
2^03^0 & 2^13^0 & 2^23^0 & 2^33^0 & 2^43^0 & 2^53^0 & 2^63^0  \\
2^03^1 & 2^13^1 & 2^23^1 & 2^33^1 & 2^43^1 & 2^53^1 & 2^63^1 & \\
2^03^2 & 2^13^2 & 2^23^2 & 2^33^2 & 2^43^2 & 2^53^2 & 2^63^2 & \\
2^03^3 & 2^13^3 & 2^23^3 & 2^33^3 & 2^43^3 & 2^53^3 & 2^63^3
\end{matrix}$$
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