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A general practice, even among very primitive people, is to use twigs. If you gnaw on a twig, its end will fray; then you can use the frayed end as a sort of a brush. If you ever do a lot of camping, you learn this very fast.
Ancient Romans used tooth powder such as pumice or very fine sand and linen cloth. They also used various cleansers and astringents like vinegar. Another popular cleaner was urine.