Finding the Greatest Common Factor: A Prime Adventure!

Mathematics Grades 4th Grade 4:46 Video
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Lesson Description

Learn how to find the Greatest Common Factor (GCF) of two numbers using prime factorization. This lesson makes finding the biggest shared factor fun and easy!

Video Resource

Greatest Common Factor (GCF)

Professor Dave Explains

Duration: 4:46
Watch on YouTube

Key Concepts

  • Factors: Numbers that divide evenly into another number.
  • Prime Factorization: Breaking down a number into its prime number components.
  • Greatest Common Factor (GCF): The largest factor shared by two or more numbers.

Learning Objectives

  • Students will be able to define 'factor' and 'Greatest Common Factor'.
  • Students will be able to find the GCF of two numbers by listing all factors.
  • Students will be able to find the GCF of two numbers using prime factorization.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of a 'factor'. Ask students for examples of factors of different numbers (e.g., factors of 6 are 1, 2, 3, and 6). Introduce the concept of 'common factors' by asking students to find factors that are shared between two numbers (e.g., common factors of 6 and 9 are 1 and 3).
  • Video Viewing (10 mins)
    Play the Professor Dave Explains video on Greatest Common Factors. Encourage students to take notes on the two methods explained: listing factors and using prime factorization.
  • Listing Factors Practice (10 mins)
    Provide students with pairs of small numbers (e.g., 8 and 12, 15 and 20). Have them list all the factors of each number and then identify the Greatest Common Factor. Discuss their findings as a class.
  • Prime Factorization Method (15 mins)
    Review the concept of prime factorization. Guide students through the process of finding the prime factorization of several numbers. Then, demonstrate how to use prime factorization to find the GCF of two numbers, as shown in the video. Emphasize the step of identifying common prime factors and multiplying them together.
  • Independent Practice (10 mins)
    Provide students with a worksheet containing problems where they need to find the GCF of two numbers using the prime factorization method. Include some larger numbers to emphasize the efficiency of this method.

Interactive Exercises

  • GCF Bingo
    Create bingo cards with numbers on them. Call out pairs of numbers and have students find the GCF. If the GCF is on their bingo card, they mark it off. The first student to get bingo wins.

Discussion Questions

  • What is a factor?
  • What does 'greatest common factor' mean?
  • Which method for finding the GCF do you prefer: listing factors or prime factorization? Why?

Skills Developed

  • Factor identification
  • Prime factorization
  • Problem-solving

Multiple Choice Questions

Question 1:

What is a factor of a number?

Correct Answer: A number that divides evenly into the number.

Question 2:

What does GCF stand for?

Correct Answer: Greatest Common Factor

Question 3:

What is the GCF of 6 and 9?

Correct Answer: 3

Question 4:

What is prime factorization?

Correct Answer: Breaking a number down into its prime number factors.

Question 5:

Which of these is NOT a factor of 12?

Correct Answer: 5

Question 6:

The prime factors of 10 are:

Correct Answer: 2 and 5

Question 7:

To find the GCF using prime factorization, you...

Correct Answer: Find the prime factors that are in BOTH lists and multiply them together.

Question 8:

What is the GCF of 4 and 8?

Correct Answer: 4

Question 9:

What is a prime number?

Correct Answer: A number that can only be divided by 1 and itself.

Question 10:

Why is prime factorization helpful when finding the GCF of big numbers?

Correct Answer: It's easier than listing all the factors.

Fill in the Blank Questions

Question 1:

A ______ is a number that divides evenly into another number.

Correct Answer: factor

Question 2:

The largest factor that two numbers share is called the ______.

Correct Answer: GCF

Question 3:

Breaking a number down into its prime factors is called prime ______.

Correct Answer: factorization

Question 4:

The GCF of 12 and 18 is ______.

Correct Answer: 6

Question 5:

A ______ number can only be divided evenly by 1 and itself.

Correct Answer: prime

Question 6:

The prime factors of 14 are 2 and ______.

Correct Answer: 7

Question 7:

To find the GCF using prime factorization, you find the prime factors that are in ______ lists.

Correct Answer: both

Question 8:

The GCF of 5 and 10 is ______.

Correct Answer: 5

Question 9:

We can use ______ or listing factors to find the GCF.

Correct Answer: factorization

Question 10:

The first step in prime factorization is to find the ______ numbers that divide the given number.

Correct Answer: prime

Educational Standards

4.N.2.1:[Objective] Demonstrate fluency with multiplication and division facts with factors up to 12. 4.N.2.2:[Objective] Multiply 3-digit by 1-digit and 2-digit by 2-digit whole numbers, using various strategies, including but not limited to standard algorithms. 4.N.2.5:[Objective] Use strategies and algorithms (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties) based on knowledge of place value, equality, and properties of operations to divide a 3-digit dividend by a 1-digit whole number divisor, with and without remainders.

Teaching Materials

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