Warm-upWarm-upFind the prime factorization for the following:Find the prime factorization for the following:

1)1) 56 2) 75 3) 110 4) 9056 2) 75 3) 110 4) 90

5) What is a number divisible by 5) What is a number divisible by 2,3,4,5,6,8,9,and 10? (Answers 2,3,4,5,6,8,9,and 10? (Answers may vary)may vary)

Warm-up AnswerWarm-up Answer

1) 21) 233 * 7 * 7

2) 3 * 52) 3 * 522

3) 2 * 5 * 113) 2 * 5 * 11

4) 2 * 34) 2 * 322 * 5 * 5

VocabularyVocabulary

Greatest common factorGreatest common factor (GCF) – the (GCF) – the largest common factor of two or more largest common factor of two or more given numbersgiven numbers

Greatest Common Factor (GCF)Greatest Common Factor (GCF)

What is a factor?What is a factor?

There are two methods to find the GCFThere are two methods to find the GCF LIST METHODLIST METHOD PRIME FACTORIZATION METHODPRIME FACTORIZATION METHOD

Greatest Common Factor (GCF)Greatest Common Factor (GCF)

1 - LIST METHOD1 - LIST METHOD List all the factors of each numberList all the factors of each number Circle the greatest factor that is all the listsCircle the greatest factor that is all the lists

Greatest Common Factor (GCF)Greatest Common Factor (GCF)

2 – PRIME FACTORIZATION METHOD2 – PRIME FACTORIZATION METHOD Write the prime factorization of each Write the prime factorization of each

number and circle the common prime number and circle the common prime factorsfactors

Multiply the common prime factorsMultiply the common prime factors

Something else to think about . . .Something else to think about . . .

With the prime factorization method, you can With the prime factorization method, you can figure out the GCF using exponential form.figure out the GCF using exponential form.

22² x 3 x 5² x 3 x 5

2³ x 3² x 5 x 72³ x 3² x 5 x 7

Use the powers they have in common.Use the powers they have in common.

So they share 2² and 3 and 5. Now multiply So they share 2² and 3 and 5. Now multiply these together and get 60—the GCF.these together and get 60—the GCF.

Greatest Common Factor (GCF)Greatest Common Factor (GCF)

EXAMPLE 1: Find the GCF using a list.EXAMPLE 1: Find the GCF using a list.

a. 28 and 42a. 28 and 42

Greatest Common Factor (GCF)Greatest Common Factor (GCF)

EXAMPLE 1: Find the GCF using a list.EXAMPLE 1: Find the GCF using a list.

b. 12, 36, and 54b. 12, 36, and 54

Greatest Common Factor (GCF)Greatest Common Factor (GCF)

EXAMPLE 2: Find the GCF using prime EXAMPLE 2: Find the GCF using prime factorization.factorization.

a. 30, 56a. 30, 56

Greatest Common Factor (GCF)Greatest Common Factor (GCF)

EXAMPLE 2: Find the GCF using prime EXAMPLE 2: Find the GCF using prime factorization.factorization.

a. 45, 18, 27a. 45, 18, 27

Greatest Common Factor (GCF)Greatest Common Factor (GCF)

EXAMPLE 3: Jenna has 16 red flowers and 24 yellow EXAMPLE 3: Jenna has 16 red flowers and 24 yellow flowers. She wants to make bouquets with the same flowers. She wants to make bouquets with the same number of each color flower in each bouquet. What is number of each color flower in each bouquet. What is the great number of bouquets she can make?the great number of bouquets she can make?

Greatest Common Factor (GCF)Greatest Common Factor (GCF)

Now you try…find the GCF of the set of Now you try…find the GCF of the set of numbers:numbers:

1)1) 12 and 1512 and 15 2) 36 and 452) 36 and 45

HOMEWORKHOMEWORKGCF Crossword PuzzleGCF Crossword Puzzle