2-Way Prime Factorization

Worksheet Description

This worksheet is a two-part educational exercise on prime factorization. In the first part, students are given nine numbers and are instructed to write the prime factorization for each. The second part flips the task, providing six sets of prime factors for which students must identify the original composite number. The layout is structured with each number and set of factors clearly presented in its own box, leaving space for students to write the corresponding answers.

The worksheet’s first section teaches students how to break down composite numbers into their prime components, a process essential for understanding the building blocks of the number system. The second section reinforces this concept by requiring students to reverse the process, thereby solidifying their understanding of how prime factors combine to form composite numbers. This dual approach not only enhances multiplication and division skills but also fosters critical thinking as students switch between factorization and synthesis of numbers. These skills are foundational for advanced mathematical concepts like least common multiples and greatest common divisors.