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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. When thinking about finding the Greatest Common Factor, or the GCF… THINK BACKWARDS F … F ind the Factors C … C ircle Common Factors

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Greatest Common Factor (GCF)

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  1. Greatest Common Factor (GCF)

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

  3. 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)

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

  5. Important to Remember… There are TWO methods for finding the GCF of two or more numbers… Method 1…UseBook Ends Method 2…UsePrime Factorization Greatest Common Factor (GCF)

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

  7. Finding the GCF: Method 1 – Book Ends Example 1: Find the GCF of 24 and 36. Greatest Common Factor (GCF) Step 1: Find the factors of each number. 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

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

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

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

  11. Finding the GCF: Method 1 – Book Ends Example 2: Find the GCF of 12 and 24. Greatest Common Factor (GCF) Step 1: Find the factors of each number. 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

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

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

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

  15. Finding the GCF: Method 1 – Book Ends Example 3: Find the GCF of 16 and 20. Greatest Common Factor (GCF) Step 1: Find the factors of each number. 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

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

  17. Finding the GCF: Method 2 – Prime Factorization Example 3: Find the GCF of 16 and 20. Greatest Common Factor (GCF) Step 1: Find the prime factorization of each number. Step 2: Find the product of the common prime factors 16 20 16: 2 · 2 · 2 · 2 20: 2 · 2 · 5 2 8 2 10 2 2 5 4 2 · 2 = 4 2 2 GCF = 4 2 · 2 · 2 · 2 2 · 2 · 5

  18. Important to Remember… There are TWO methods for finding the GCF of two or more numbers… Method 1…UseBook Ends Method 2…UsePrime Factorization Greatest Common Factor (GCF)

  19. Guided Practice Problems Directions: Find the GCF of each set of numbers. 1. 9, 12, 30 2. 42, 60 3. 48, 64 4. 40a2b, 48ab4 Greatest Common Factor (GCF)

  20. Guided Practice Problems Directions: Find the GCF of each set of numbers. 1. 9, 12, 30 => 3 2. 42, 60 => 6 3. 48, 64 => 16 4. 40a2b, 48ab4=> 8ab Greatest Common Factor (GCF)

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