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Knowing students difficulties in using the concept of division and divisibility is one of the basic needs to design genetic decomposition of that concept. This article is a report from qualitative research that discusses conceptual issues about the idea of division and divisibility given by prospective mathematics teacher students who use the APOS theory. The data for the study were collected from an interview conducted on 3 pre-service mathematics teachers in their second year and who have attended and completed a test on the division and divisibility in an elementary number theory course. These participants were selected based on their performance in the test. However, the interview conducted showed that there are five difficulties involved and they include solving the divisibility problem on integers, algebraic manipulation and structure sense, distinguishing between variables and parameters on division problem presented in algebraic expression, associating between division algorithm and definition, and application of divisibility properties and theorems.