[size=200]PART A[/size] Wait. it's possible to have an odd number of divisors? For divisor, there is always another divisor that pairs it up! So that means it must be an even number! Oh yeah? What if I told you this.... What if the other divisor that pairs it up is the same number! :what?: How about this: How many factors does $4$ have? $$1,2,4$$ Oooooooh. So that means if the amount of divisors is an odd number, it must be a perfect square, right? (end of conversation) Now let's go look at some exceptions. $$16$$ Now this fits the circumstances of being a perfect square, but does it fit the circumstances of having three positive divisors? $$\text{divisors of 16}=1,2,4,8,16$$ FIVE?! AW CMON! Let's look at this more in depth. $$16$$ $$16=4^2$$ $$16=(2\cdot 2)^2$$ AHA! We know what happened! The square root was a composite number, therefore we could break it down more! So that means The square root can't be a composite number...... ...