CONFIDENTIAL 1

GREATEST COMMON FACTOR

CONFIDENTIAL 2

LET’S CHECK WHAT WE KNOW

1. Tell whether each number is divisible by 2, 3, 4, 5, 6, 9 or 10.

1. 67 2. 145 3. 891 4. 202

2. Find the Prime factorization of:

i) 63 ii) 8 iii) 120 iv) 264 v) 28

CONFIDENTIAL 3

FACTORS

• When a number divides another number exactly, the first number is called the factor of the second.

• 1 is a factor of every number.

• The greatest factor of the number is the number itself.

• If a number can divide another number leaving no remainder, it is a factor.

FACTOR FACTS

CONFIDENTIAL 4

FINDING FACTORS

Find the factors of 24

Since 1 is a factor of every number, it is a factor of 24.

24 ÷ 2 = 12; 24 ÷ 3 = 8; 24 ÷ 4 = 6; 24 ÷ 6 =4;

24 ÷8 = 3; 24 ÷ 12 = 2.

Also, 24 is the factor of itself.

Therefore, the factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

Finding factors is easy

CONFIDENTIAL 5

Do some problems to find factors

• Find the factors of the following numbers:

1. 36

2. 42

3. 35

4. 33

5. 21

Let’s do it !

CONFIDENTIAL 6

Use of a Venn Diagram to represent common factors

• A Venn Diagram uses overlapping circles to show the similarities and differences of two groups of items. Any item that is located where the circles overlap has a characteristic of both circles.

CONFIDENTIAL 7

Representation of Factors and Common factors in a Venn Diagram

• The Venn Diagram below shows the common factors of 12 and 18

Factors of 18Factors of 12

4

12

9 18 1, 2

3, 4

The common factors are 1, 2, 3, 4.

CONFIDENTIAL 8

Finding Common Factors• Find the common factors using

Venn Diagram:

1. 9 and 15

2. 18 and 24

3. 15 and 35

CONFIDENTIAL 9

Greatest Common Factor (GCF)

• Numbers often have common factors. The greatest of the common factors of two or more numbers is the Greatest Common Factor (GCF) of the numbers.

CONFIDENTIAL 10

Have a break !!!

CONFIDENTIAL 11

How to find the greatest common factor

• Find the GCF of 8 and 12

Factors of 8 Factors of 12

8 1

2 4

3

6

12

The common factors are 1, 2, 4.

The greatest common factor among them is 4

CONFIDENTIAL 12

Try to do it

• Find the GCF with the help of Venn Diagram

a. 48 and 96

b. 35 and 60

c. 12 and 13

CONFIDENTIAL 13

Finding the GCF by Listing Factors• Find the GCF of 20 and 30

Factors of 20

1, 20

2, 10

4, 5

Factors of 30

1, 30

2, 15

3, 10

5, 6

The common factors are 1, 2, 5 and 10.

The greatest among them is 10.

GCF = 10

CONFIDENTIAL 14

Now your turn

• Find the GCF of the following by listing the factors:

1. 25 and 28

2. 15 and 30

3. 24 and 48

CONFIDENTIAL 15

Find the GCF by using Prime Factors• Find the GCF of 20 and 35

Method 1

20

2 10

2 52

35

5 7

The common factor is 5 and GCF is 5

20, 35

4 , 7

5

Method 2

Divide 20 and 35 by 5

Since we will not be able to divide 4 and 7 with the same number, 5 is the GCF

CONFIDENTIAL 16

Let’s look at another example!

36 and 24 share two 2’s and one 3 in common.

GCF: 12

36: 2, 2, 3, 3 24: 2, 2, 2, 3

CONFIDENTIAL 17

• The GCF of two or more numbers is the product of the common prime factors of the numbers.

• Example: Find the GCF of 18 and 24

GCF of two or more numbers

2 18, 24

3 9, 12

3, 4 The quotients cannot be divided further by a common prime factor

GCF = 2X3 = 6

CONFIDENTIAL 18

Now try to do it

• Find the GCF by prime factorization method:

i) 36, 48

ii) 72, 81

iii) 99,110

CONFIDENTIAL 19

What is hidden?

• http://www.thekidzpage.com/onlinejigsawpuzzles/kids-jigsaw-puzzles/12-piece-jigsaw/08-08-06-spider.html

Title: Format: WebEx Web BrowserDouble-click to edit

CONFIDENTIAL 20

Practice Problems

I. Find the GCF with the help of Venn Diagrams

a) 10, 30

b) 12,18

II. Find the GCF by listing factors:

a) 18, 42

b) 16, 52, 76

III. Find the GCF by prime factorization:

a) 36, 90

b) 9, 18, 42

Wow!!!

CONFIDENTIAL 21

Use GCF to solve real life situations

• Mr. Stephan has 4 storage cases that can hold 16, 24,36 and 48 files. The cases have sections holding the same number of files. What is the greatest number of files in a section?

2 16, 24, 36

2 8, 12, 18

4, 6, 9 The quotients cannot be divided further by a common prime factor

The greatest number of files in a section is 4

CONFIDENTIAL 22

Solve this problem with GCF

• Mohammed wants to put 45 rose plants, 81 orchids and 63 hibiscus plants in his garden. If he puts the same number of plants in each row and each row has only type of plant. What is the greatest number of plants he can put in one row?

How to do this?

Hmmm…..

CONFIDENTIAL 23

Assignment

1) 9, 18 and 42

Find the GCF using Venn Diagram

Find the GCF by Listing Factors

2) 12, 36, 48

Find the GCF by Prime Factorization

3) 27, 54, 18

I can do it…

CONFIDENTIAL 24

Review • Greatest Common FactorGreatest Common Factor

The greatest of the common factors of two or more numbers is the Greatest Common Factor (GCF) of the numbers.

• There are two ways to find GCF:− Make a list of factors− Use Prime Factorization

CONFIDENTIAL 25

Great Job!