yield beta and conversion factor

When do we ignore the figures while calculating number of contracts. I saw a question that didn’t use yield beta even though CF was used. The question gave duration of Future contract

Yield on bond = Beta * (Yield on CTD). If it’s not given, assume it’s 1.

This is a future contract on treasury bond

The cirriculumn has the formular of hedge ration using yield beta. Technically, you can use the yield beta to calculate the number of future contract.

Are there any other multiplicative figures that need incorporated aside from CF/yield beta (if applicable)? I feel like I saw something else in an old mock but wanted to get here before pouring over 8 years worth of old tests.

thanks

Hedge ratio: (DD_P/DD_CTD) * conversion factor for the CTD * yield beta