List all factors of 𝑝 squared 𝑞.
These factors will be expressions that divide evenly into 𝑝 squared 𝑞. And then when multiplied together, they would give us back 𝑝 squared 𝑞. Now I’m not multiplying all the factors altogether at once together. However, there could be a combination of some that would give us back 𝑝 squared 𝑞.
So let’s begin with things that would go into 𝑝 squared 𝑞 evenly: one, 𝑝, 𝑝 squared, and then two would be the highest exponent that we could go for 𝑝. So now let’s begin with 𝑞. 𝑞 and then that’s it for 𝑞. There is no 𝑞 squared. There aren’t enough 𝑞s for 𝑞 squared to go into that evenly.
So now we could put one 𝑝 and one 𝑞 together into 𝑝 squared 𝑞. And then to make that a little larger, we can have 𝑝 squared and 𝑞 go into there evenly. And this will be it. This will be all of the expressions that would go evenly into 𝑝 squared 𝑞. So these would be all of our factors.