This article describes an exciting exploration-based activity in which students develop an alternative definition of factor that can help them solve problems like the one presented above. Students work in groups to collect data, analyze the data to make conjectures, and then spend a significant amount of time debating and justifying their conjectures. Although designed for prospective teachers, the activity can be modified for middle school classrooms. Details are given about how to implement the activity in a middle school classroom as well as what we learned from past enactments with prospective elementary teachers. It concludes with a discussion of the activity's potential to impact students' related work with greatest common factors (GCF) and least common multiples (LCM).