Hmm although I suck when it comes to math I will try my level best here
As i've already explained Class A is Network.Node.Node.Node
Now what is a IP address? Its a 32 it[4 byte] long address.
What does this mean?Each byte is equal to 8 bits.
Thus how many node addresses can the Class A address have?
2^24 [i.e 2 raise to the power 24]Why because the first byte makes the network id,the rest three bytes make the host id which equals to 24bits.So you want to find the hosts aint it?
2^24=16,777,216
You may ask why 2 raise to n? Simple because a bit is either a 1 or a 0.
Similarly just follow the network classes classification for Class B & Class C & you will finally end at those numbers without any confusion.