REMEMBER:

What is a factor?

What are the factors of 24?

Common Factors:

1, 2, 4 and 8

What is the Greatest Common Factor (GCF)?

First, what is a Common Factor?

It is a number that is a factor of two or more numbers .

Example:

Factors of 24:

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

1, 2, 4, 5, 8, 10, 20, 40Factors of 40

Find the common factors of:

a)3 and 12

b)6 and 18

c)10 and 20

d)24 and 40

e)8 and 20

Common Factors :Common Factors :

So, What is the Greatest Common Factor (GCF)?

The greatest common factor is the BIGGEST

FACTOR that is common to two or more numbers

Find the GCF of 40 and 24

24: 40:

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

1, 2, 4, 5, 8, 10, 20, 40What’s the biggest common factor?

8

Example:

How can you find the GCF?

There are different methods, let’s check two of them.

Method 1: Listing the factors

a) Find all the Factors of each number,b) Circle the Common factors,c) Choose the Greatest of those

Factors of 12 are 1, 2, 3, 4, 6 and 12

Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30

GCF: 6

Example 1 : Factors of 12 and 30

Example 2: The factors of 24 are

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

The factors of 36 are

1, 2, 3, 4, 6, 9, 12, 18, 36

The common factors of 24 and 36 are

1, 2, 3, 4, 6, 12

The Greatest Common Factor of 24 and 36 is 12

GCF(24, 36) = 12

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

The common factors are 1, 2, 3, 4, 6, and 12.

ANSWER

EXAMPLE 3

The greatest common factor of 48, 24, and 36 is 12.

1, 2, 3, 4, 6,

1, 2, 3, 4, 6,

1, 2, 3, 4, 6, 12

12

12The GCF is 12.

Now, Practice: List the factors. Then, find the GCF.

We can find the GCF of two or more numbers by listing out the factors of each and

identifying the largest common factor

But, this could be difficult when the numbers are very

large.

Method 2: Prime Factorization

Another way to find the greatest common factor of two or more numbers is to use the prime

factorization of each number.

"Prime Factorization" is finding which prime numbers multiply together to make the original

number.

The product of the common prime factors is the greatest common factor (GCF).

Using prime factorization (factor trees)

Example 1: Find the GCF of 36 and 48

36 48

6 6

2 3 2 3

86

2 4

2 3 2 2 2

36:

48:

2•2•3•3

2•2•2•2•3

a) Find the common factors are 2,2,and 3

The GCF is 2•2•3 12

b) Multiply them.

It is best to start working from the smallest prime number,

Find the greatest common factor of 180 and 126 using prime factorization.

Begin by writing the prime factorization of each number.

180

10 18

2 5 2 9

2 5 2 3 3

126

2 63

2 3 21

2 3 3 7

180 = 2 2 3 3 5

126 = 2 3 3 7

ANSWER

The common prime factors of 180 and 126 are 2, 3, and 3.

Using Prime Factorization to Find the GCFEXAMPLE 2

So, the greatest common factor is 2x3x3 = 18.

Practice: Find the GCF using prime factorization