Looking Through the Lens: Constructing and Verifying the GCD

This GeoGebra example uses a “lens”-style view to visualize how integers can be decomposed into factors, guiding learners to find and verify the greatest common factor (GCF). It centers on key number-theory ideas: Factors, PrimeFactors (prime factorization), and GCD, along with the related understanding of divisibility that connects to LCM. The construction is driven by the provided GeoGebra elements: Textfield inputs (inputBox1, inputBox2, inputBox3) for integers such as a, b, c; Factors to generate factor lists (stored in list1 and shown alongside explanatory texts like text1/text2/text3); PrimeFactors to compute prime decompositions; and GCD to compute the greatest common divisor. Supporting objects include matrix1, matrix2, matrix3 and intermediate variables (d, e, f, g, h) to organize and display intermediate results, with button1 to trigger the computation and update the visualization. Suitable for middle/high school teaching (divisibility, factorization, and introductory number theory) and interactive classroom demonstrations.