In this lesson, students are introduced to common factors of two whole numbers as factors that both numbers share and the greatest common factor as the largest of these shared factors. Students reason abstractly and quantitatively as they see factors as representing the different ways to divide a certain number of books evenly (MP2). They make use of structure when they notice how factor pairs help ensure that all possible combinations have been found (MP7). Common factors represent the ways to combine two different types of books in one box, and the greatest common factor represents the largest number of combination boxes possible. Students also relate the greatest common factor to the size of the largest square that can tile a rectangle with given dimensions without gaps or overlaps.