Greatest common factor
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GREATEST COMMON FACTOR. 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. FACTOR FACTS. FACTORS.

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GREATEST COMMON FACTOR

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Greatest common factor

GREATEST COMMON FACTOR

CONFIDENTIAL


Let s check what we know

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


Factors

FACTOR FACTS

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.

CONFIDENTIAL


Finding factors

Finding factors is easy

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

CONFIDENTIAL


Do some problems to find factors

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

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

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

Finding Common Factors

  • Find the common factors using Venn Diagram:

  • 9 and 15

  • 18 and 24

  • 15 and 35

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Greatest common factor gcf

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.

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Have a break

Have a break !!!

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How to find the greatest common factor

How to find the greatest common factor

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

CONFIDENTIAL


Try to do it

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


Finding the gcf by listing factors

Finding the GCF by Listing Factors

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

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

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Find the gcf by using prime factors

Find the GCF by using Prime Factors

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

CONFIDENTIAL


Greatest common factor

Let’s look at another example!

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

GCF of two or more numbers

  • 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

CONFIDENTIAL


Now try to do it

Now try to do it

  • Find the GCF by prime factorization method:

  • 36, 48

  • 72, 81

  • 99,110

CONFIDENTIAL


What is hidden

What is hidden?

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

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Practice problems

Practice Problems

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

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?

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

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…..

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Assignment

Assignment

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

CONFIDENTIAL


Review

Review

  • 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

CONFIDENTIAL


Great job

Great Job!

CONFIDENTIAL


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