If so, what is that number and why can't you divide the public key by G to obtain the private key?
No sufficiently efficient algorithm for division is known. Multiplication over a closed group is a lossy process.
For an imperfect analogy, consider multiplication over the group of 100-digit numbers where you just keep the last 100 digits of the result. Since you don't know what digits were discarded, you can't naively reverse a multiplication.
The corresponding algorithm in DSA is modular exponentiation --
(G^X) mod n, which is also, for practical purposes with large numbers, irreversible even if G and n are known.
Uncompressed "G" is 0479BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8
The "04" at the beginning is simply added (for what reason I don't know).
The first 64 hex characters after the "04" supposedly represent the "x" value and the last 64 hex characters supposedly represent the "y" value.
I don't know the specifics of why it cannot be reversed (I am also seeking the answer to that question).
Note that the "multiplication" in question is not ordinary integer multiplication, but elliptic curve point multiplication.
The whole point of working over an elliptic curve in this way is that multiplication is easy, but division is hard.