Single registration vs multiple registration

If a Firm has PAN India operations but centralised office for billing

1. Then is there any requirement for multiple registration in each state having operations as Billing is from some central Office.

2. If Registration is required for each state then how will we allocate the Input credit of Office which is minimal amount

REquirement to get registered in GST come on what criteria

1. Location of Business operation, OR

2. Location of our clients to whom we invoice, OR

3. or Both.

Please give us the clarity on registration issue.

Thanks in anticipation