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Hi there and welcome
This is 100% a scam.This is what is known as "phone phishing" it is can be a very serious problem if you do let them access your computer.
Basically what they will do is say that you have problems. Any actual computer problems you have will be entirely coincidental. Usually what they will do is show you the Windows error log which always shows a lot of errors but these are normal and on all windows computers, they are not viruses.
Next they log onto your computer and lie to you about the numerous problems they pretend to find. Next they will attempt to get you to pay a few hundred dollars to "fix" the issues when in fact they actually do nothing too helpful.
Always remember, no legitimate tech support company would ever do business in such a manner.
You were wise to end the call.