Topics
1. Number Sense
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United States of America
Grade 6

1.03 Factors and greatest common factor (GCF)

Lesson
Practice

Introduction

In previous years, we have identified primes, composites and  factor pairs  . In this lesson we will apply what we know about factor pairs to learn about the greatest common factor (GCF). Later on we can apply this concept to other topics in mathematics such as fractions and rational numbers.

Greatest common factor (GCF)

Some numbers can share the same factor. For example 2 is a factor of 10 and 24. We call the number 2 in this situation a common factor. When we are asked to find the greatest common factor (GCF) between two or more numbers, we are being asked to find the biggest factor that the numbers have in common. In other words, we want to find the number that all the numbers can be divided by that leaves no remainder in each case (or leftovers).

Examples

Example 1

Consider the numbers 36 and 4.

a

List all the factors of 36.

Worked Solution
Create a strategy

Write down all the numbers that 36 is divisible by.

Apply the idea

The factors of 36 are:1,\,2,\,3,\,4,\,6,\,9,\,12,\,18,\,36

b

List all the factors of 4.

Worked Solution
Create a strategy

Write down all the numbers that 4 is divisible by.

Apply the idea

The factors of 4 are:1,\,2,\,4

c

Now find the greatest common factor of 36 and 4.

Worked Solution
Create a strategy

We can consider all the common factors of 36 and 4 and choose the greatest number that appears in the list.

Apply the idea

The factors of 36 are: 1,\,2,\,3,\,4,\,6,\,9,\,12,\,18,\,36

The factors of 4 are: 1,\,2,\,4

The numbers that appear in both factor lists are: 1,\,2,\,4

The largest number in the list is the GCF, 4.

Example 2

What is the greatest common factor of 115 and 55?

Worked Solution
Create a strategy

We can consider all the common factors of 115 and 55, and choose the greatest number that appears in the list.

Apply the idea

The factors of 115 are: 1,\,5,\,23,\,115

The factors of 55 are: 1,\,5,\,11,\,55

The numbers that appear in both factor lists are: 1,\,5

The largest number in the list is the GCF, 5.

Idea summary

The greatest common factor of two or more numbers is the biggest number that they can be divided by without remainders.

Outcomes

6.NS.B.4

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

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