Understanding Greatest Common Factor through Prime Factorization

The video tutorial by Mr. J explains how to find the greatest common factor (GCF) of three numbers using prime factorization. It covers the step-by-step process of breaking down the numbers 54, 36, and 90 into their prime factors. The tutorial then demonstrates how to identify common prime factors and multiply them to find the GCF, which is 18 in this example. This method is particularly useful for larger numbers where listing all factors is impractical.

What is the main advantage of using prime factorization to find the GCF of larger numbers?

• It requires less mathematical knowledge.

• It is faster than listing all factors.

• It is more accurate.

• It is easier to understand.

What is the first step in the prime factorization of 54?

• Divide by 3

• Divide by 2

• Divide by 9

• Divide by 5

After dividing 54 by 2, what is the next step in its prime factorization?

• Divide 27 by 5

• Divide 27 by 2

• Divide 27 by 9

• Divide 27 by 3

What is the first factor used in the prime factorization of 36?

• 9

• 5

• 3

• 2

What is the result of dividing 36 by 2 in the prime factorization process?

• 12

• 6

• 9

• 18

What is the first factor used in the prime factorization of 90?

• 3

• 2

• 9

• 5

After dividing 90 by 2, what is the next step in its prime factorization?

• Divide 45 by 2

• Divide 45 by 5

• Divide 45 by 3

• Divide 45 by 9

Which of the following is a common prime factor of 54, 36, and 90?

• 7

• 9

• 2

• 5

What is the greatest common factor of 54, 36, and 90?

• 36

• 24

• 18

• 12

How do you calculate the GCF once you have the common prime factors?

• Add them together

• Multiply them together

• Subtract them

• Divide them