Greatest Common Factor (GCF). Essential Question: How do I find the greatest common factor of two or...

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.


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


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


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


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


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


Finding the GCF: Method 2 – Prime Finding the GCF: Method 2 – Prime FactorizationFactorization


Step 1: Find the prime factorization of each number.Step 2: Find the product of the common prime factors



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




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




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





1616: 1, 2, : 1, 2, 44, 8, 16, 8, 16

2020: 1, 2, : 1, 2, 44, 5, 10, 20, 5, 10, 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


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


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


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


Homework

p.162 #20-30, even, 34, 36


Greatest Common Factor (GCF). Essential Question: How do I find the greatest common factor of two or...

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