Interesting question. A *lot* depends on the pattern you select. However, by Googling info on the net I came up with the following calculations.
Assume a king size quilt is 112" x 120". Assume you can cut six 6-1/2" squares from a fat quarter. Assume the quilt is made up of 6"-finished size squares.
For this quilt, you would need about 380 squares (112/6=19 squares across, 120/6=20 squares down, 19x20=380 squares). Since you can cut six squares from a fat quarter, you would need 380/6=64 fat quarters minimum. It does not allow for tossing fabrics you don't like, or don't go with your design, and it does not allow for miscuts or fabrics that shrink (if you prewash), and it does not provide for either backing fabric or binding fabric.
If you are super-new to quilting, I highly recommend that you do not start with a king-size or queen-size quilt. A crib quilt or lap quilt would be best.
I'm not that keen on buying fat quarters because they can be difficult to put together if they are all different colors and designs. If I were to make a scrap quilt using fat quarters (say, like an Irish Chain pattern, which I love), I would buy half the fabric in a background I liked and cut only half the quilt from fat quarters.