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Discovering frequent factors from long strings is an important problem in many applications, such as biosequence mining. In classical approaches, the algorithms process a vast database of small strings. However, in this paper we analyze a small database of long strings. The main difference resides in the high number of patterns to analyze. To tackle the problem, we have developed a new algorithm for discovering frequent factors in long strings. This algorithm uses a new data structure to arrange nodes in a trie. A positioning matrix is defined as a new positioning strategy. By using positioning matrices, we can apply advanced prune heuristics in a trie with a minimal computational cost. The positioning matrices let us process strings including Short Tandem Repeats and calculate different interestingness measures efficiently. The algorithm has been successfully used in natural language and biological sequence contexts.