The fact that we know we have a great great grandfather. Is the reasoning we use for this inductive or deductive?
You don't use induction, because induction is impossible:
Some deduction may be involved in working out the consequences of existing biological knowledge. That knowledge was created by noticing problems with previous ideas, guessing solutions to the problems and then criticising the guesses until only one is left and it has no known criticisms.
You did not in fact use any reasoning at all. You stated a fact. The reasoning is involved in the justification of that fact, which was not included. It could be any justification at all. Some popular ones include:
Deductive logic: If you start from the claim that every person has a father (and elide any issues of Adam and Eve for a moment), it's easy to argue that every person has a grandfather, and a great grandfather, and a great great grandfather. Taking that last claim, "every person has a great great grandfather" and "I am a person" you can deduce that "I have a great great grandfather."
Inductive logic: If you are certain that you have a father, and that they have a father, you may induce that probably every one of your ancestors had a father, and we can build a chain out of them. So long as you're comfortable assuming that chain is long enough, you can recognize that you must have someone in the "great great grandfather" position.
Abduction: It's entirely possible that you don't have a great great grandfather at all. You might be a test-tube baby from entirely synthetic sources with no paternal lineage to speak of who was adopted under conditions of absolute secrecy. Of course, that hypothesis seems much less likely than the one that when your father says he had a father before him, and so on and so forth, and your great great grandfather's name was Joe, and lived from 1819-1887 and is burred in Kentucky. So, you may use abduction to assume that the most likely hypothesis is indeed true. Thus, you have a great great great grandfather.
You don't actually mention the reasoning, so it's difficult to say what type of reasoning you are using. I'm guessing that you mean abductive, which basically means reasoning to the best explanation. It's generally used in science - where we take the evidence we have and formulate the best explanation we can.
In this example, you would presumably look around and see that people are related to one another, that parents produce babies - that sort of thing.