All deliverable bonds are not uniform but differ in terms of coupon, maturity and consequently price. The conversion factor is needed to adjust for the price a bond with certain covenants would have. Imo this is given by the clearing agency. With that conversion factor you can determine the theoretical futures price.
The CTD is the bond which shows the cheapest price and is calculated (at delivery) by dividing the cash price of the bond by the conversion factor. If you´ll have to deliver, you take the bond with the smallest price.
The nominal underlying bond in a T-bond contract is a 6% coupon, 20-years-to-maturity Treasury bond.
There aren’t any such creatures in the market today.
To get around this obstacle, they allow you to deliver any T-bond with at least 15 years to maturity (or first call); there are a number of such bonds in the market. Because there are many such bonds – all with different coupon rates and different maturities; hence, different market prices – it would be unfair to the long if the short could deliver $100,000 par of bond A with a market price of $90,000, when the market price of $100,000 par of the nominal (6%, 20-year) would be $105,000; the long would lose (and the short would gain) $15,000. To try to correct for this, each bond has a conversion factor; the conversion factor for bond A would be $90,000 / $105,000 = 0.857142. Thus, to deliver bond A against a $100,000 (par) T-bond contract, short would have to deliver $116,667 (= $100,000 / 0.857142) par.
Every eligible bond has a conversion factor, but the factors aren’t perfect (because the market price keeps changing, but the conversion factors aren’t recomputed with every bond transaction; I believe that they’re recomputed once per day). Therefore, when it’s time to deliver a bond, one of the eligible bonds will be the cheapest: the market price divided by the conversion factor for that bond will be lower than for any other eligible bond. That bond is the CTD.
The differences in the values you would have to deliver are not big (the conversion factors do a pretty good job): I’d be surprised if there were a 1% difference between the cheapest-to-deliver and the most-expensive-to-deliver.