11/29/1111/29/11

• Turn in any make up work you completed over the break!

• Bellringer: Write down one thing about your break.

• Turn in any make up work you completed over the break!

• Bellringer: Write down one thing about your break.

Finding The Greatest Common Factor

Finding The Greatest Common Factor

Greatest Common Factor

Greatest Common Factor

The greatest common factor is the largest common factor of two numbers.

Factors are all of the numbers that divide into a given number equally.

The greatest common factor can be found by comparing all the factors of two numbers or by finding the prime factorization of two numbers

The greatest common factor is the largest common factor of two numbers.

Factors are all of the numbers that divide into a given number equally.

The greatest common factor can be found by comparing all the factors of two numbers or by finding the prime factorization of two numbers

Finding FactorsFinding Factors

Find the factors of 18 1 goes into 18, 18 times. 2 goes into 18, 9 times. 3 goes into 18, 6times.

4 does not divide 18 evenly. 5 does not divide 18 evenly.

We are now back to 6. We have found all factors of 18.

1, 2, 3, 6, 9, and 18

Find the factors of 18 1 goes into 18, 18 times. 2 goes into 18, 9 times. 3 goes into 18, 6times.

4 does not divide 18 evenly. 5 does not divide 18 evenly.

We are now back to 6. We have found all factors of 18.

1, 2, 3, 6, 9, and 18

Finding The GCF Using Factors

Finding The GCF Using Factors

Determine the greatest common factor of two numbers by finding

all the factors for the two numbers then comparing them. The largest common factor of the

two numbers is their greatest common factor.

Determine the greatest common factor of two numbers by finding

all the factors for the two numbers then comparing them. The largest common factor of the

two numbers is their greatest common factor.

Think Backwards…Think Backwards…

•Find Factors•Circle Common Factors•Group Greatest Factor

•Find Factors•Circle Common Factors•Group Greatest Factor

Step 1: Find the FactorsStep 1: Find the Factors

• 24 – 1,2,3,4,6,8,12,24• 36 – 1,2,3,4,6,9,12,18,36

• 24 – 1,2,3,4,6,8,12,24• 36 – 1,2,3,4,6,9,12,18,36

Step 2: Circle Common Factors

Step 2: Circle Common Factors

• 24 – 1,2,3,4,6,8,12,24• 36 – 1,2,3,4,6,9,12,18,36

• 24 – 1,2,3,4,6,8,12,24• 36 – 1,2,3,4,6,9,12,18,36

Step 3: Group the Greatest Factor

Step 3: Group the Greatest Factor

• 24 – 1,2,3,4,6,8,12,24• 36 – 1,2,3,4,6,9,12,18,36

• 24 – 1,2,3,4,6,8,12,24• 36 – 1,2,3,4,6,9,12,18,36

The Greatest Common Factor of 24 and 36 is…The Greatest Common Factor of 24 and 36 is…

1212

Find the GCF of 12 and 24

Find the GCF of 12 and 24

• Step 1: Find the factors

• 12 – • 24 –

• Step 1: Find the factors

• 12 – • 24 –

Find the GCF of 12 and 24

Find the GCF of 12 and 24

• Step 2: Circle the common factors

• 12 – 1,2,3,4,6,12• 24 –

1,2,3,4,6,8,12,24

• Step 2: Circle the common factors

• 12 – 1,2,3,4,6,12• 24 –

1,2,3,4,6,8,12,24

Find the GCF of 12 and 24

Find the GCF of 12 and 24

• Step 3: Group the greatest factor

• 12 – 1,2,3,4,6,12• 24 –

1,2,3,4,6,8,12,24

• Step 3: Group the greatest factor

• 12 – 1,2,3,4,6,12• 24 –

1,2,3,4,6,8,12,24

The Greatest Common Factor of 12 and 24 is …The Greatest Common

Factor of 12 and 24 is …

1212

Using Factors Again Using Factors Again

Find the GCF of 15 and 100

Factors of 15:Factors of 100:

The greatest common factor of 15 and 100 is

Find the GCF of 15 and 100

Factors of 15:Factors of 100:

The greatest common factor of 15 and 100 is

Your turn!Your turn!

• Find the Greatest Common Factor of 16 and 20.

• Remember…Find Factors, Circle Common, Group Greatest!

• Find the Greatest Common Factor of 16 and 20.

• Remember…Find Factors, Circle Common, Group Greatest!

The Greatest Common Factor of 16 and 20 is…The Greatest Common Factor of 16 and 20 is…

44

Exit TicketExit Ticket

• What is the GCF of 15 and 30?• What is the GCF of 15 and 30?

11/3011/30

• Get out your homework.• Bellringer:

• Multiply WITHOUT A CALCULATOR!• 5x6• -4x3• -7x-6

• Get out your homework.• Bellringer:

• Multiply WITHOUT A CALCULATOR!• 5x6• -4x3• -7x-6

Homework answersHomework answers

1. 42. 53. 84. 15. 4

1. 42. 53. 84. 15. 4

Finding the Prime Factorization

Finding the Prime Factorization

A prime factorization is when a product is broken down until only prime numbers remain. Prime numbers are numbers who’s only factors are 1 and them self. A factor tree is useful in finding a prime factorization.

A prime factorization is when a product is broken down until only prime numbers remain. Prime numbers are numbers who’s only factors are 1 and them self. A factor tree is useful in finding a prime factorization.

Prime FactorizationPrime Factorization

Break 18 down to only prime numbers. 18/\

2 9 /\

3 3

18 = 2 × 3 × 3

Break 18 down to only prime numbers. 18/\

2 9 /\

3 3

18 = 2 × 3 × 3

Finding the GCF Using Prime Factorization

Finding the GCF Using Prime Factorization

To determine the greatest common factor, find the prime factorization

for each number. Find all of the common prime factors of the two

numbers and multiply them together. Your sum is the GCF.

To determine the greatest common factor, find the prime factorization

for each number. Find all of the common prime factors of the two

numbers and multiply them together. Your sum is the GCF.

Using Prime FactorizationUsing Prime

FactorizationFind the GCF of 36 and 24

36 24 /\ /\

Find the GCF of 36 and 24 36 24 /\ /\

Using Prime Factorization Again

Using Prime Factorization Again

Find the GCF of 21 and 42 21 42

Find the GCF of 21 and 42 21 42

GCF worksheetGCF worksheet

• Complete questions 6-10.• Complete questions 6-10.