# Lesson 16

Common Factors

### Lesson Narrative

In this lesson, students use contextual situations to learn about common factors and the greatest common factor of two whole numbers. They develop strategies for finding common multiples and least common multiples. They develop a definition of the terms common factor and greatest common factor for two whole numbers (MP6).

### Learning Goals

Teacher Facing

• Comprehend (orally and in writing) the terms “factor,” “common factor,” and “greatest common factor.”
• Explain (orally and in writing) how to determine the greatest common factor of two whole numbers less than 100.
• List the factors of a number and identify common factors for two numbers in a real-world situation.

### Student Facing

Let’s use factors to solve problems.

### Required Preparation

For the first classroom activity, "Diego's Bake Sale," provide access to two different colors of snap cubes (48 of one color and 64 of the other) for students who would benefit from manipulatives. For students with visual impairment, provide access to manipulatives that are distinguished by their shape rather than color.

In the second classroom activity, "Greatest Common Factor," it may be helpful for some students to have access to graph paper to make rectangles that will help them find all possible factors of a whole number.

### Student Facing

• I can explain what a common factor is.
• I can explain what the greatest common factor is.
• I can find the greatest common factor of two whole numbers.

### Glossary Entries

• common factor

A common factor of two numbers is a number that divides evenly into both numbers. For example, 5 is a common factor of 15 and 20, because $$15 \div 5 = 3$$ and $$20 \div 5 = 4$$. Both of the quotients, 3 and 4, are whole numbers.

• The factors of 15 are 1, 3, 5, and 15.
• The factors of 20 are 1, 2, 4, 5, 10, and 20.
• greatest common factor

The greatest common factor of two numbers is the largest number that divides evenly into both numbers. Sometimes we call this the GCF. For example, 15 is the greatest common factor of 45 and 60.

• The factors of 45 are 1, 3, 5, 9, 15, and 45.
• The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.