Greatest Common Factor (GCF)

Question 1

Factors are numbers that are multiplied together to give a product.

Ex. factors of 18: 1, 2, 3, 6, 9, 18

Common factors are factors that are the SAME for 2 or more numbers.

Ex. factors of 12: 1, 2, 3, 4, 6, 12 factors of 18: 1, 2, 3, 6, 9, 18

The greatest common factor is the largest of the common factors.

Ex. What’s the GCF for the numbers 12 and 18? _______

Answer 1

Ex. What’s the GCF for the numbers 12 and 18? 6

Question 2

You can also use prime factorization (factor trees) to help you discover the GCF.

Let’s practice using factor trees for 12 and 18. Keep breaking apart composite numbers and dropping down the prime numbers.

Steps:

1. Write the prime factorization.
   12 =____ 18 = ____

Find the common factors. 3. Find the product of those prime factors.

Since each number has one 2 and one 3 in common, ______ would be the GCF.

Answer 2

You can also use prime factorization (factor trees) to help you discover the GCF.

Let’s practice using factor trees for 12 and 18. Keep breaking apart composite numbers and dropping down the prime numbers.

Steps:

1. Write the prime factorization.
   12 = 2 x 2 x 3 18 = 2 x 3 x 3

Find the common factors. 3. Find the product of those prime factors.

Since each number has one 2 and one 3 in common, 6 would be the GCF.

Question 3

Let’s practice one in a word problem: Ex. There are 16 boys and 24 girls in Mr. Carney’s gym class. The students must form groups to rotate through stations. Each group must have the same number of boys and the same number of girls. What is the greatest number of groups Mr. Carney can make if every student must be in a group?
Whenever you see GREATEST number of groups, that means to find the greatest common factor of the numbers
This year we are going to use Method 2: Prime Factorization

Since each number has three ____ in common, the GCF would be _____ because ( ___ x___ x____ = ____ )

Answer 3

Let’s practice one in a word problem: Ex. There are 16 boys and 24 girls in Mr. Carney’s gym class. The students must form groups to rotate through stations. Each group must have the same number of boys and the same number of girls. What is the greatest number of groups Mr. Carney can make if every student must be in a group?
Whenever you see GREATEST number of groups, that means to find the greatest common factor of the numbers
This year we are going to use Method 2: Prime Factorization

Since each number has three 2 in common, the GCF would be 8 because ( 2 x 2 x 2 = 8 )