Greatest Common Factor (GCF)

Standard M6N1 Students will understand the meaning of the four arithmetic operations as related to positive rational numbers and will use these concepts to solve problems. b. Determine the greatest common factor (GCF) and the least common multiple (LCM) for a set of numbers.

How are GCF and LCM applied to fractions? Essential Questions How are GCF and LCM applied to fractions?

The GCF of two or more numbers is the greatest number that is a factor of each number

1) Listing the Factors 2) Prime Factorization 3) Ladder method Three ways to find GCF: 1) Listing the Factors 2) Prime Factorization 3) Ladder method

Step 1: List the factors of the numbers 1) Listing the Factors Step 1: List the factors of the numbers

Example: 24 and 36 36 24 1 24 2 12 3 8 4 6 1 36 2 18 3 12 4 9 6 6

Step 2: List the common factors (the numbers that are in both lists).

Common Factors of 24 & 36 are: 1, 2, 3, 4, 6, 12

The largest is the greatest common factor: 12

Step 1: For each number draw a factor tree 2) Prime Factorization Step 1: For each number draw a factor tree

Example: 24 and 36 36 24 4 6 6 6 2 3 2 2 2 3 2 3 12 • • 2 2 3 =

Using the Prime Factorization Method: The GCF is also 12

3) Ladder method 2 144 48 2 72 24 2 36 12 6 18 6 1 3 1

Multiply all common factors from outside of divided by box Multiply all common factors from outside of divided by box. 2 x 2 x 2 x 6 x 1= GCF 48

Find the Greatest Common Factor for the following: 1) 8 and 24 2) 15 and 45

Answers 1) GCF is 8 2) GCF is 15

Find the GCF 36 and 54 72 and 120 14 and 33 108 and 132