Dollar Duration of a Futures Contract receiving, guess, conversion, something, contract

Chuckrox8

To find the numbers of futures contract needed to achieve a target duration:

numbers of contract = (DDt - DDp) / (DDctd / conversion factor)

Why do we need to divide DDctd by the conversion factor? Since the futures contracts that we will be receiving are the cheapest to deliver contracts and have a duration of DDctd, wouldn't the formula (DDt - DDp) / DDctd work to find the numbers of futures contract we want? I guess I am missing / misunderstanding something.

Any insights and comments are appreciated!