Post on 17-Jan-2016
Greatest Greatest Common Common
Factor (GCF)Factor (GCF)
Essential Question:Essential Question:How do I find the greatest common How do I find the greatest common
factor of two or three numbers, factor of two or three numbers, and why is this relevant to me?and why is this relevant to me?
Common Core Objective:Common Core Objective:6.NS.46.NS.4
Common Core Objective:Common Core Objective:Students will be able to identify the greatest Students will be able to identify the greatest
common factors of two or three one, two, common factors of two or three one, two, and three digit numbers with 80% and three digit numbers with 80% accuracy.accuracy.
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
Vocabulary: Factor – a number that divides into a
whole number with a remainder of zero. Greatest Common Factor – the largest
factor that two or more numbers have in common.
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
When thinking about finding the When thinking about finding the Greatest Common Factor, or the Greatest Common Factor, or the
GCF…GCF…
THINK BACKWARDSTHINK BACKWARDS
FF……FFind the Factorsind the Factors
CC……CCircle Common Factorsircle Common Factors
GG……GGroup Largest Factorroup Largest Factor
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
But if that’s too hard…But if that’s too hard…
Simply THINKSimply THINK
GG……GGreatest (largest)reatest (largest)
CC……CCommon (shared)ommon (shared)
FF……FFactoractor
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
Important to Remember…Important to Remember…
There are There are TWOTWO methods for methods for
finding the GCF of two or more finding the GCF of two or more numbers…numbers…
Method 1…Method 1…UseUse Book EndsBook Ends
Method 2…Method 2…UseUse Prime FactorizationPrime Factorization
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
Finding the GCF: Method 1 – Book EndsFinding the GCF: Method 1 – Book EndsExample 1Example 1:: Find the GCF of 24 and 36. Find the GCF of 24 and 36.
Step 1: Find the factors of each number.
Step 2: Circle the common factors of the numbersStep 3: Group or circle the largest factor they have in common
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
Finding the GCF: Method 1 – Book EndsFinding the GCF: Method 1 – Book Ends
Example 1Example 1:: Find the GCF of 24 and 36. Find the GCF of 24 and 36.
Step 1: Find the factors of each number.
Step 2: Circle the common factors of the numbersStep 3: Group or circle the largest factor they have in common
2424: 1, 2, 3, 4, 6, 8, 12, : 1, 2, 3, 4, 6, 8, 12, 24243636: 1, 2, 3, 4, 6, 9, 12, 18, : 1, 2, 3, 4, 6, 9, 12, 18, 3636
The GCF of 24 and 36 is 12
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
Finding the GCF: Method 2 – Prime Finding the GCF: Method 2 – Prime FactorizationFactorization
Example 1Example 1:: Find the GCF of 24 and 36. Find the GCF of 24 and 36.
Step 1: Find the prime factorization of each number.Step 2: Find the product of the common prime factors
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
Finding the GCF: Method 2 – Prime Finding the GCF: Method 2 – Prime FactorizationFactorization
Example 1Example 1:: Find the GCF of 24 and 36. Find the GCF of 24 and 36.Step 1: Find the prime factorization of each number.Step 2: Find the product of the common prime factors2424 3636
GCF = 12
22 121266
2 · 2 · 2 · 32 · 2 · 2 · 3 2 · 2 · 3 · 32 · 2 · 3 · 3
2222 33
33 12126622
33 22
2424: : 22 · · 22 · 2 · · 2 · 333636: : 22 · · 22 · 3 · · 3 · 33
2 · 2 · 3 = 2 · 2 · 3 = 1212
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
Finding the GCF: Method 1 – Book EndsFinding the GCF: Method 1 – Book Ends
Example 2Example 2:: Find the GCF of 12 and 24. Find the GCF of 12 and 24.
Step 1: Find the factors of each number.Step 2: Circle the common factors of the numbersStep 3: Group or circle the largest factor they have in common
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
Finding the GCF: Method 1 – Book EndsFinding the GCF: Method 1 – Book Ends
Example 2Example 2:: Find the GCF of 12 and 24. Find the GCF of 12 and 24.
Step 1: Find the factors of each number.Step 2: Circle the common factors of the numbersStep 3: Group or circle the largest factor they have in common
1212: : 1, 2, 3, 4, 6, 1, 2, 3, 4, 6, 1212
2424: 1, 2, 3, 4, 6, 8, : 1, 2, 3, 4, 6, 8, 1212, , 2424
The GCF of 12 and 24 is 12
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
Finding the GCF: Method 2 – Prime Finding the GCF: Method 2 – Prime FactorizationFactorization
Example 2Example 2:: Find the GCF of 12 and 24. Find the GCF of 12 and 24.Step 1: Find the prime factorization of each number.Step 2: Find the product of the common prime factors
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
Finding the GCF: Method 2 – Prime Finding the GCF: Method 2 – Prime FactorizationFactorization
Example 2Example 2:: Find the GCF of 12 and 24. Find the GCF of 12 and 24.Step 1: Find the prime factorization of each number.Step 2: Find the product of the common prime factors
1212 2424
GCF = 12
22 66
2 · 2 · 32 · 2 · 3 2 · 2 · 3 · 32 · 2 · 3 · 3
22 3322 1212
662222 33
1212: : 22 · · 22 · · 332424: : 22 · · 22 · 2 · · 2 · 33
2 · 2 · 3 = 2 · 2 · 3 = 1212
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
Finding the GCF: Method 1 – Book EndsFinding the GCF: Method 1 – Book Ends
Example 3Example 3:: Find the GCF of 16 and 20. Find the GCF of 16 and 20.
Step 1: Find the factors of each number.Step 2: Circle the common factors of the numbersStep 3: Group or circle the largest factor they have in common
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
Finding the GCF: Method 1 – Book EndsFinding the GCF: Method 1 – Book Ends
Example 3Example 3:: Find the GCF of 16 and 20. Find the GCF of 16 and 20.
Step 1: Find the factors of each number.Step 2: Circle the common factors of the numbersStep 3: Group or circle the largest factor they have in common
1616: 1, 2, : 1, 2, 44, 8, 16, 8, 16
2020: 1, 2, : 1, 2, 44, 5, 10, 20, 5, 10, 20
The GCF of 16 and 20 is 4
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
Finding the GCF: Method 2 – Prime Finding the GCF: Method 2 – Prime FactorizationFactorization
Example 3Example 3:: Find the GCF of 16 and 20. Find the GCF of 16 and 20.
Step 1: Find the prime factorization of each number.Step 2: Find the product of the common prime factors
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
Finding the GCF: Method 2 – Prime Finding the GCF: Method 2 – Prime FactorizationFactorization
Example 3Example 3:: Find the GCF of 16 and 20. Find the GCF of 16 and 20.Step 1: Find the prime factorization of each number.Step 2: Find the product of the common prime factors
1616 2020
GCF = 4
22 88
2 · 2 · 52 · 2 · 5
22 4422 1010
22 55
2020: : 22 · · 22 · 5 · 5
2 · 2 = 42 · 2 = 422 22
2 · 2 · 2 · 2 · 2 · 2 · 22
1616: : 22 · · 22 · 2 · · 2 · 22
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
Important to Remember…Important to Remember…
There are There are TWOTWO methods for methods for
finding the GCF of two or more finding the GCF of two or more numbers…numbers…
Method 1Method 1……UseUse Book EndsBook Ends
Method 2Method 2……UseUse Prime FactorizationPrime Factorization
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
Guided Practice ProblemsGuided Practice ProblemsDirectionsDirections:: Find the GCF of each set of Find the GCF of each set of
numbers.numbers.
1. 9, 12, 301. 9, 12, 30
2. 42, 602. 42, 60
3. 48, 643. 48, 64
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
Guided Practice ProblemsGuided Practice ProblemsDirectionsDirections:: Find the GCF of each set of Find the GCF of each set of
numbers.numbers.
1. 9, 12, 301. 9, 12, 30 => => 33
2. 42, 602. 42, 60 => => 66
3. 48, 643. 48, 64 => => 1616
Greatest Common Factor Greatest Common Factor (GCF)(GCF)
Homework
p.162 #20-30, even, 34, 36
Greatest Common Factor Greatest Common Factor (GCF)(GCF)