Is it okay to give employers my SSN during an interview?

I just got home from an interview. The interview went just as normal as ever, but after the usual questions and handshakes, they told me HR requested for information such as my address and my SSN. They had not yet offered me a position. Would it have been safe to give my SSN at that point? Would you guys give it in this situation? Any help would be appreciated. Thank you.

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