Greatest Common Factor and Prime Factorization

The video tutorial by Mr. J explains how to find the greatest common factor (GCF) of three numbers using two methods: listing factors and prime factorization. The first method involves listing all factors of the numbers 27, 9, and 18, and identifying the largest common factor. The second method uses prime factorization to find the GCF of the numbers 54, 36, and 90. Mr. J provides step-by-step examples for each method, highlighting the importance of understanding factors and prime numbers in determining the GCF.

What is the greatest common factor (GCF)?

• The product of two or more numbers.

• The smallest number that divides two or more numbers.

• The largest number that divides two or more numbers.

• The sum of two or more numbers.

Which of the following is NOT a strategy to find the GCF?

• Using multiplication tables

• Adding the numbers

• Prime factorization

• Listing out factors

When listing factors, why is it suggested to start with 1 and the number itself?

• Because they are always prime numbers.

• Because they are the easiest to remember.

• Because they are the smallest and largest factors.

• Because they are the only factors.

What are the common factors of 27, 9, and 18?

• 1, 3, 9

• 3, 6, 9

• 1, 2, 3

• 2, 3, 6

Why might prime factorization be preferred for larger numbers?

• It is more fun to do.

• It requires less mathematical knowledge.

• It is the only method that works.

• It is faster and more efficient.

What is the first step in prime factorization?

• Multiply the number by 2.

• Break down the number into its prime factors.

• Add all the numbers together.

• Divide the number by 1.

Which of the following is a prime factor of 54?

• 4

• 8

• 6

• 2

What is the GCF of 54, 36, and 90 using prime factorization?

• 12

• 18

• 24

• 30

What is the purpose of finding common prime factors in prime factorization?

• To find the smallest common multiple.

• To multiply them to get the GCF.

• To add them together.

• To divide them by the largest number.

Which method might be more time-consuming for larger numbers?

• Listing out factors

• Neither, both are quick

• Prime factorization

• Both are equally time-consuming