MGSE6.NS.4

Greatest Common Factor (GCF)

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MGSE6.NS.4 Find the common multiples of two whole numbers less than or equal to 12 and the common factors of two whole numbers less than or equal to 100. a. Find the greatest common factor of 2 whole numbers and 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 factors. (GCF) Example: 36 + 8 = 4(9 + 2) b. Apply the least common multiple of two whole numbers less than or equal to 12 to solve real-world problems.

​Standard

​Learning Targets

• I can find factor pairs of any numbers between 1 and 100.

• I can explain what the greatest common factor is.

• I can find the greatest common factor of two numbers less than or equal to 100.

​Vocabulary

1. Factor

2. Prime Factorization

3. Factor Tree

4. Greatest Common Factor

Essential Question: What is the Greatest Common Factor used for?

To simplify fractions (and algebra later in math)

A number or variable that can be multiplied with another number or variable to produce the given term​

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​What is a Factor?

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Finding which prime factors multiply to create the actual number

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Prime Factorization

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A diagram that shows all the factors of a given number​

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Factor Tree

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Multiple Choice

What does GCF stand for?

• Good Common Factor

• Greatest Common Factor

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Divisibility Rules: Shortcuts to help determine if numbers are factors of a number.

• 2 - is the last digit an even number

• 3 - is the sum of the digits divisible by 3

• 4 - are the last 2 digits divisible by 4

• 5 - is the last digit a 0 or 5

• 6 - is the number divisible by both 2 and 3

• 9 - is the sum of the digits divisible by 9

• 10 - is the last digit a 0

Steps to find the GCF:

• Find ALL factors of each number.

• Write the factors in numerical order from least to greatest.

• Find the common factors (CF)

• The greatest of the common factors is the GCF.

• Show all work in a neat and orderly way.

One way we find the Greatest Common Factor between two numbers is by LISTING and IDENTIFYING

Listing Method

• 16 = 1, 2, 4, 8, 16

• 24 = 1, 2, 3, 4, 6, 8, 12, 24

• If we will compare the list of factors of 16 and 24, we can identify the common factors.

• GCF is the highest common factor that appears on the list.

• The GCF of 16 and 24 is 8.

Multiple Choice

What is the Greatest Common Factor of 40 and 100?

• 20

• 10

• 5

• 1

Another way to find GCF is by the LADDER METHOD

Multiple Choice

What is the GCF of 15 and 20?

• 2

• 0

• 1

• 5

Multiple Choice

What is the GCF of 9 and 4?

• 0

• 1

• 3

• 5

Poll

Do you understand today's lesson?

• Yes, I totally got this!

• I have no idea how to do this.

• I need to practice a little to understand better.