Visualizing Why HCF Determines Squares Fitting a Rectangle

This interactive GeoGebra activity demonstrates why the highest common factor (HCF) of a rectangle's length and breadth gives the side length of the largest square that can tile the rectangle perfectly. It visualizes the relationship between factors, common factors, and square tiling. The construction uses Textfield and InputBox for user input of length and breadth, Polygon to draw the rectangle, Sequence and If to generate and arrange square grids, and RotateText for labeling. Key objects include pic1, A, l, b, s, B, C, D, q1, a, b_1, c, d, E, q2, e, f, g, h, l1, l2, i, j, k, l3, sqfitlength, sqfitbreadth, text2, text3, text4, m, text5, n, text7, text1, button1, button2, and isGCD. Suitable for upper primary and middle school students learning factors and HCF, and for teachers to illustrate the concept geometrically before formal number theory.