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GREATEST COMMON FACTOR

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GREATEST COMMON FACTOR

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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

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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.

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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

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Do some problems to find factors

- Find the factors of the following numbers:
- 36
- 42
- 35
- 33
- 21

Let’s do it !

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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.

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Representation of Factors and Common factors in a Venn Diagram

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

4

1, 2

3, 4

9

18

12

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

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Finding Common Factors Diagram

- Find the common factors using Venn Diagram:
- 9 and 15
- 18 and 24
- 15 and 35

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Greatest Common Factor (GCF) Diagram

- 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.

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Have a break !!! Diagram

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How to find the greatest common factor Diagram

Factors of 8

Factors of 12

- Find the GCF of 8 and 12

1

2 4

3

6

12

8

The common factors are 1, 2, 4.

The greatest common factor among them is 4

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Try to do it Diagram

- Find the GCF with the help of Venn Diagram
a. 48 and 96

b. 35 and 60

c. 12 and 13

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Finding the GCF by Listing Factors Diagram

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

The greatest among them is 10.

GCF = 10

- Find the GCF of 20 and 30

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Now your turn Diagram

- Find the GCF of the following by listing the factors:
1. 25 and 28

2. 15 and 30

3. 24 and 48

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Find the GCF by using Prime Factors Diagram

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

35

20

- Find the GCF of 20 and 35
Method 1

10

5

7

2

2

2

5

5

20, 35

4 , 7

The common factor is 5 and GCF is 5

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Let’s look at another example! Diagram

36: 2, 2, 3, 3

24: 2, 2, 2, 3

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

GCF: 12

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GCF of two or more numbers Diagram

- 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

The quotients cannot be divided further by a common prime factor

GCF = 2X3 = 6

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Now try to do it Diagram

- Find the GCF by prime factorization method:
- 36, 48
- 72, 81
- 99,110

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What is hidden? Diagram

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

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Practice Problems Diagram

Wow!!!

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

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Use GCF to solve real life situations Diagram

- 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?

The quotients cannot be divided further by a common prime factor

The greatest number of files in a section is 4

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Solve this problem with GCF Diagram

- 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…..

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Assignment Diagram

Find the GCF using Venn Diagram

I can do it…

1) 9, 18 and 42

Find the GCF by Listing Factors

2) 12, 36, 48

Find the GCF by Prime Factorization

3) 27, 54, 18

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Review Diagram

- Greatest 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

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Great Job! Diagram

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