Finding GCF and LCM through Prime Factorization

This video tutorial explains how to use prime factorization to find the greatest common factor (GCF) and the least common multiple (LCM) of two numbers. The instructor demonstrates the process with two examples: first using the numbers 28 and 16, and then 12 and 20. The video emphasizes identifying common prime factors to determine the GCF and using remaining factors to calculate the LCM.

What is the first step in finding the greatest common factor (GCF) and least common multiple (LCM) of two numbers?

• Divide the larger number by the smaller number

• Subtract the smaller number from the larger number

• Find the prime factorization of each number

• Add the two numbers

What are the prime factors of 28?

• 2, 14

• 1, 28

• 2, 2, 7

• 4, 7

What is the greatest common factor (GCF) of 28 and 16?

• 16

• 4

• 2

• 8

Which of the following is NOT a step in finding the least common multiple (LCM) of two numbers?

• Circle the prime factors that are left over

• Multiply the circled prime factors

• Add the prime factors together

• Include the GCF in the multiplication

What is the least common multiple (LCM) of 28 and 16?

• 140

• 112

• 84

• 56

What are the prime factors of 12?

• 1, 12

• 2, 6

• 3, 4

• 2, 2, 3

What is the greatest common factor (GCF) of 12 and 20?

• 10

• 6

• 4

• 2

Which of the following is a prime factor of 20?

• 10

• Both 2 and 5

• 5

• 2

What is the least common multiple (LCM) of 12 and 20?

• 40

• 60

• 80

• 100

Which of the following steps is necessary to find the LCM after finding the GCF?

• Multiply the GCF by the remaining prime factors

• Add the GCF to the remaining prime factors

• Divide the GCF by the remaining prime factors

• Subtract the GCF from the remaining prime factors