Greatest Common Factor GCF Greatest Common Factor GCF

Greatest Common Factor (GCF)

Greatest Common Factor (GCF) Vocabulary: § Greatest Common Factor – the largest factor that two or more numbers have in common.

Greatest Common Factor (GCF) When thinking about finding the Greatest Common Factor, or the GCF… THINK BACKWARDS F…Find the Factors C…Circle Common Factors G…Group Largest Factor

Greatest Common Factor (GCF) But if that’s too hard… Simply THINK G…Greatest (largest) C…Common (shared) F…Factor

Greatest Common Factor (GCF) Important to Remember… TWO There are methods for finding the GCF of two or more numbers… Method 1…Use Book Ends Method 2…Use Prime Factorization

Greatest Common Factor (GCF) Finding the GCF: Method 1 – Book Ends Step 1: Find the each. GCF number. Example 1: factors Findofthe of 24 and 36. Step 2: Circle the common factors of the numbers Step 3: Group or circle the largest factor they have in common

Greatest Common Factor (GCF) Finding the GCF: Method 1 – Book Ends Step 1: Find the each. GCF number. Example 1: factors Findofthe of 24 and 36. Step 2: Circle the common factors of the numbers Step 3: Group or circle the largest factor they have in common 24: 1, 2, 3, 4, 6, 8, 12, 24 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 The GCF of 24 and 36 is 12

Greatest Common Factor (GCF) Finding the GCF: Method 2 – Prime Factorization Example 1: prime Findfactorization the GCF of 24 and 36. Step 1: Find the of each number. Step 2: Find the product of the common prime factors

Greatest Common Factor (GCF) Finding the GCF: Method 2 – Prime Factorization Example 1: prime Findfactorization the GCF of 24 and 36. Step 1: Find the of each number. Step 2: Find the product of the common prime factors 24 2 1 22 6 2 3 2· 2· 2· 3 36 2 1 22 6 3 3 2· 2· 3· 24: 2 · 2 · 36 36: 2 · 3 · 3 2· 2· 3= 12 GCF = 12

Greatest Common Factor (GCF) Finding the GCF: Method 1 – Book Ends Step 1: Find the each. GCF number. Example 2: factors Findofthe of 12 and 24. Step 2: Circle the common factors of the numbers Step 3: Group or circle the largest factor they have in common

Greatest Common Factor (GCF) Finding the GCF: Method 1 – Book Ends Step 1: Find the each. GCF number. Example 2: factors Findofthe of 12 and 24. Step 2: Circle the common factors of the numbers Step 3: Group or circle the largest factor they have in common 12: 1, 2, 3, 4, 6, 12 24: 1, 2, 3, 4, 6, 8, 12, 24 The GCF of 12 and 24 is 12

Greatest Common Factor (GCF) Finding the GCF: Method 2 – Prime Factorization Example 2: prime Findfactorization the GCF of 12 and 24. Step 1: Find the of each number. Step 2: Find the product of the common prime factors

Greatest Common Factor (GCF) Finding the GCF: Method 2 – Prime Factorization Example 2: prime Findfactorization the GCF of 12 and 24. Step 1: Find the of each number. Step 2: Find the product of the common prime factors 12 2 24 6 2 3 2· 2· 2 1 22 6 2 3 2· 2· 3· 12: 2 · 3 24: 2 · 2 · 3 2· 2· 3= 12 GCF = 12

Greatest Common Factor (GCF) Finding the GCF: Method 1 – Book Ends Step 1: Find the each. GCF number. Example 3: factors Findofthe of 16 and 20. Step 2: Circle the common factors of the numbers Step 3: Group or circle the largest factor they have in common

Greatest Common Factor (GCF) Finding the GCF: Method 1 – Book Ends Step 1: Find the each. GCF number. Example 3: factors Findofthe of 16 and 20. Step 2: Circle the common factors of the numbers Step 3: Group or circle the largest factor they have in common 16: 1, 2, 4, 8, 16 20: 1, 2, 4, 5, 10, 20 The GCF of 16 and 20 is 4

Greatest Common Factor (GCF) Finding the GCF: Method 2 – Prime Factorization Example 3: prime Findfactorization the GCF of 16 and 20. Step 1: Find the of each number. Step 2: Find the product of the common prime factors

Greatest Common Factor (GCF) Finding the GCF: Method 2 – Prime Factorization Example 3: prime Findfactorization the GCF of 16 and 20. Step 1: Find the of each number. Step 2: Find the product of the common prime factors 16 2 20 8 2 4 2 2 2· 2· 2· 2 1 20 5 2· 2· 5 16: 2 · 2 · 20: 2 · 5 2 2· 2= 4 =4 GCF

Greatest Common Factor (GCF) Important to Remember… TWO There are methods for finding the GCF of two or more numbers… Method 1…Use Book Ends Method 2…Use Prime Factorization

Greatest Common Factor (GCF) Guided Practice Problems Directions: Find the GCF of each set of numbers. 1. 2. 3. 9, 12, 30 42, 60 48, 64 4. 40 a 2 b, 48 ab 4

Greatest Common Factor (GCF) Guided Practice Problems Directions: Find the GCF of each set of numbers. 1. 2. 3. 9, 12, 30 42, 60 48, 64 => 3 => 6 => 16 4. 40 a 2 b, 48 ab 4 => 8 ab