Greatest Common Factor

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Greatest Common Factor

• 4.2

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Objective

• You will be able to find the greatest common
  factor (GCF) of two or more numbers.
• Word watch
• -common factor
• -greatest common factor (GCF)
• -relatively prime

3

• A whole number that is a factor of two or more
  whole numbers is called a common factor.
• The greatest of the common factors is called the
  greatest common factor (GCF)

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Venn diagram
A Venn diagram uses circles to show how elements
among sets of numbers or objects are related.
3
5
1 2 4
6
8
10
24
20
12
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Finding the GreatestCommon Factor

• List the factors of each number
• See which factors both numbers have in common
• The greatest of these common factors is called
  the greatest common factor!

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EXAMPLE

• Find the GCF of 20 and 24.
• First, list the factors of 20 and 24
• factors of 20 1 , 2 , 4 , 5 , 10 , 20
• factors of 24 1 , 2 , 3 , 4 , 6 , 8 , 12 , 24

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EXAMPLE

• Find the GCF of 20 and 24.
• First, list the factors of 20 and 24
• factors of 20 1 , 2 , 4 , 5 , 10 , 20
• factors of 24 1 , 2 , 3 , 4 , 6 , 8 , 12 , 24
• The common factors are 1 , 2 , and 4 so the GCF
  is 4!

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YOUR TURN!!

• Find the GCF of 21, 42, 63
• Factors of
• 21 1 , 3 , 7 , 21
• 42 1 , 2 , 3 , 6 , 7 , 14 , 21 , 42
• 63 1 , 3 , 7, 9 , 21, 63

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YOUR TURN!!

• Find the GCF of 21, 42, 63
• Factors of
• 21 1 , 3 , 7 , 21
• 42 1 , 2 , 3 , 6 , 7 , 14 , 21 , 42
• 63 1 , 3 , 7 , 9 , 21 , 63
• So the GCF is?!?!?!
• 21

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Using Prime Factors

• Find the GCF of 18 and 48
• First write the prime factorization for each
  number
• 18
• / \
• 3 6
• / / \
• 3 2 3

48
/ \
12 4
/ \ / \
3 4 2 2
/ / \ \ \
3 2 2 2 2
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Using Prime Factors

• Find the GCF of 18 and 48
• First write the prime factorization for each
  number
• 18 48
• / \ /
  \
• 3 6 12 4
• / / \ / \
  / \
• 3 2 3 3 4 2
  2
• / /
  \ \ \
• 3 2 2
  2 2

The common prime factors are 2 and 3. So, the
GCF of 18 and 48 is 2 x 3, or 6.
18 2 x 3 x 3 48 2 x 2 x 2 x 2 x 3
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YOUR TURN!

• Find the GCF of 24 and 60 using prime factors
• 24
  60
• / \
  / \
• 6 4 6
  10
• / \ / \ / \
  / \
• 2 3 2 2 2 3 5
  2
• 24 2 x 2 x 2 x 3
• 60 2 x 2 x 3 x 5

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YOUR TURN!

• Find the GCF of 24 and 60 using prime factors
• 24
  60
• / \
  / \
• 6 4 6
  10
• / \ / \ / \
  / \
• 2 3 2 2 2 3 5
  2
• 24 2 x 2 x 2 x 3
• 60 2 x 2 x 3 x 5

The common prime factors are 2, 2, and 3. So,
the GCF of 24 and 60 is 2 x 2 x 3, or 12.
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• Two or more whole numbers are relatively prime if
  their GCF is 1.

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Tell whether the numbers are relatively prime

• 28 and 45
• Factors of 28 1, 2, 4, 7, 14, 28
• Factors of 45 1, 3, 5, 9, 15, 45

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Tell whether the numbers are relatively prime

• 28 and 45
• Factors of 28 1, 2, 4, 7, 14, 28
• Factors of 45 1, 3, 5, 9, 15, 45
• The GCF is 1.
• Because the GCF is 1, 28 and 45 are relatively
  prime.

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Tell whether the numbers are relatively prime

• 15 and 51
• Factors of 15 1, 3, 5, 15
• Factors of 51 1, 3, 17, 51

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Tell whether the numbers are relatively prime

• 15 and 51
• Factors of 15 1, 3, 5, 15
• Factors of 51 1, 3, 17, 51
• GCF is 3
• Because the GCF is 3, 15 and 51 are NOT
  relatively prime!

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• Any questions?!?!

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ThOuGhT oF tHe DaY

• A dragonfly has a life span of 24 hours