Prime Factorization Lesson Plan


Ever wondered how every time you swipe your credit card, buy something online, or tell a secret with a messaging app, your data is protected from hackers?

Prime factorization powers the cryptography that keeps you safe.

Use this artistic, real-life lesson plan to teach your students about prime factorization. Students will learn material with artistic guided notes, practice and check for understanding with doodle math and mazes, and wrap up with the real life application of prime factorization for cryptography.

Get the Lesson Materials

Prime Factorization — Guided Notes, Doodle Math, Color by Number, Application

Prime Factorization — Guided Notes, Doodle Math, Color by Number, Application


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Learning Objectives

After this lesson, students will be able to:

  • Differentiate between prime numbers and composite numbers

  • Use factor trees to decompose a composite number into the products of its prime factors

  • Represent prime factorization using exponents (i.e. 125 = 5^3)

  • Describe how prime factorization is used in the real world for cryptography


Before this lesson, students should be familiar with:

  • Basic multiplication and division skills

  • Understanding of the concepts of factors and multiples

  • Basic understanding of fractions and decimals (optional, but helpful)


1 hour


Key Vocabulary

  • Prime factorization

  • Composite numbers

  • Prime numbers

  • Least common denominator

  • Cryptography

Curriculum Standards


Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.


Write and evaluate numerical expressions involving whole-number exponents.


This lesson plan practices 2 and 3 digit numbers. See extensions for more practice.


Hook and Guided Notes

  • As a hook, ask students how computers keep them safe from hackers when they swipe their credit card or send a message on their phone. It all has to do with prime factorization! Refer to the last page of the guided notes as well as the FAQs below for ideas.

  • Use the guided notes to introduce the concept of prime numbers, composite numbers, and prime factorization itself. Refer to the FAQ below for a walk through on this, as well as ideas on how to respond to common student questions.

  • Introduce the steps to factor composite numbers. Then show students how to compute the prime factorization of 120 using a factor tree (120 = 2 x 2 x 2 x 3 x 5).

  • Lastly, explain how 120 = 2 x 2 x 2 x 3 x 5 can be represented in exponent form as 120 = 2^3 x 3 x 5.

Check for Understanding

  • Have students work through the problems on the check for understanding page, either collaboratively or independently.

  • Walk around and spot-check student answers on the check for understanding activity.

  • Based on student responses, reteach concepts that students need extra help with. If your class has a wide range of proficiency levels, you can pull out students for reteaching, and have more advanced students begin work on the practice exercises.


  • Have students practice prime factorization using the maze activity. Walk around to answer student questions.

  • Fast finishers can dive into the Doodle Math activity. You can assign it as homework for the remainder of the class.

Real-World Application

  • Bring the class back together, and introduce the concept of cryptography.

  • Have students wrap class by writing down writing down ways they might use prime factorization in everyday life.

And best of all—the materials for the above are included in our Prime Factorization 4-in-1 Lesson. Just print and go for an amazing lesson.


Additional practice with up to 4 digit numbers

A fun, no-prep way to practice prime factorization is our Prime Factorization with Exponents Doodle Math activity (sold separately) — it's a fresh take on color by number or color by code. It includes three levels that help students practice finding the factors of 2-, 3- and 4-digit numbers. Each answer unlocks patterns that they can doodle onto an image.

There's also a special Earth Day version of the activity (sold separately), perfect for spring.


Want to try before you buy?

Try these 6 free activities for grades 3 - 7.

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