Exploring Greatest Common Factor

• Math
• 7th Grade

Exploring Greatest Common Factor

Learning Objective

Understand the concept of greatest common factor and apply it to solve problems.

What do you already know about finding common factors?

Introduction to Common Factors

Common factors are numbers that divide two or more numbers exactly. For example, the common factors of 12 and 18 are 1, 2, 3, and 6.

Defining Greatest Common Factor

The greatest common factor (GCF) of two or more numbers is the largest number that divides each of the numbers without leaving a remainder.

Finding the GCF

To find the GCF, list all the factors of each number and identify the highest number that appears in all the lists.

GCF of Prime Numbers

When finding the GCF of prime numbers, the GCF is always 1 since prime numbers have only two factors – 1 and the number itself.

GCF Examples

Example 1: Find the GCF of 24 and 36. List factors: 24 (1, 2, 3, 4, 6, 8, 12, 24) and 36 (1, 2, 3, 4, 6, 9, 12, 18, 36). The GCF is 12.

GCF in Real Life

The concept of GCF is used in various real-life scenarios, such as simplifying fractions, reducing ingredients in recipes, and optimizing resources.

GCF and LCM Connection

The GCF and the least common multiple (LCM) are related. The product of the GCF and LCM of two numbers is equal to the product of the two numbers themselves.

Interactive Activity

Divide students into groups and provide them with pairs of numbers. Instruct them to find the GCF using the methods learned in the lesson.

Summary and Recap

Summarize the key points learned about the greatest common factor and allow students to ask any remaining questions.

Write down 3 things you learned in this lesson.

Have students enter three things they learned in this lesson. With this they can indicate their own learning efficiency of this lesson.

Write down 2 things you want to know more about.

Here, students enter two things they would like to know more about. This not only increases involvement, but also gives them more ownership.

Ask 1 question about something you haven't quite understood yet.

The students indicate here (in question form) with which part of the material they still have difficulty. For the teacher, this not only provides insight into the extent to which the students understand/master the material, but also a good starting point for the next lesson.