hand piece traceability

Hi everyone

Im looking for a bit of help/advice. I understand hand pieces need to be traceable for each individual patient. What we currently do is write the serial number of the hand piece along with the patients notes (only started this yesterday when we were told by out autoclave engineer). My question is do we also need to write down the autoclave cycle number the hand piece was sterilised on ??? also I wanted to ask we have 3 surgeries does each surgery have to have their own specific handpieces or can you share as long as you note the serial number? Many many thanks