Fact-checkers cannot manually verify every claim circulating online, so identifying which statements deserve priority is an important step in automated fact-checking. This study investigates methods for classifying statements according to their check-worthiness. It evaluates lexical features, embedding models, large language models, and traditional machine-learning classifiers using datasets containing checkable claims from tweets and political speeches. The experiments indicate that embedding- and LLM-based approaches can improve the prioritization of claims that are especially relevant for verification. The work therefore frames check-worthiness detection as a practical filtering stage that can help human fact-checkers focus limited resources on the most consequential or urgent claims.