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LESSON: Greatest Common Factors

Site: MN Partnership for Collaborative Curriculum
Course: Mathematics Essentials Q1
Book: LESSON: Greatest Common Factors
Printed by: Guest user
Date: Thursday, November 21, 2024, 3:40 PM

Description

Greatest Common Factors

Table of contents

READ: Find the Greatest Common Factor Using Lists

Find the Greatest Common Factor of Two or More Numbers Using Lists

In this lesson, you will be learning about the greatest common factor (GCF). You can figure out what the GCF is by looking at the name.

What is the greatest common factor? The greatest common factor is the greatest factor that two or more numbers have in common.

One way to finding the GCF is to make lists of the factors for two numbers and then choose the greatest factor that the two factors have in common.

Example

Find the GCF for 12 and 16.

First, we list the factors of 12 and 16.

&12 && 16\\ &12 \times 1 && 16 \times 1\\ &2 \times 6 && 8 \times 2\\ & \underline{4} \times 3 && \underline{4} \times 4

Next, we can underline the GCF.

The GCF is 4.

READ: Find the Greatest Common Factor Using Factor Trees

Find the Greatest Common Factor of Two or More Numbers Using Factor Trees

You just learned how to find the GCF by making lists. We can also find the GCF by making a factor tree. Let’s look at an example.

Example

Find the GCF of 20 and 30.

First, we make a factor tree for each number.

& \ \ \ 20 && \quad \ \ 30\\ & \ \ \big / \ \big\backslash && \quad \ \big / \ \ \big\backslash\\ & \ 4 \quad 5 && \quad 5 \ \quad 6\\ & \big / \ \big\backslash && \qquad \ \big / \ \big\backslash\\ & 2 \ \ 2 && \qquad 3 \ \ \ 2\\ & 2^2 \times 5 && 5 \times 3 \times 2

Here is a tricky one because there is more than one common factor. We have both five and two as common factors.

When you have more than one common factor, we multiply the common factors to find the GCF.

2 \times 5 = 10

10 is the greatest common factor (GCF).

EXAMPLE 1

EXAMPLE 2

EXAMPLE 3

Check Yourself! GCF