Finding The Greatest Common Factor

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Finding The Greatest Common Factor
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Greatest Common Factor

• The greatest common factor is the largest common
  factor of two numbers. Factors are all of the
  numbers that divide into a given number equally.
• The greatest common factor can be found by
  comparing all the factors of two numbers or by
  finding the prime factorization of two numbers

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Finding Factors

• Finding the factors of a number can be done by
  sequentially dividing numbers into the product.
  When the factors begin to repeat you have found
  all factors.

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Finding Factors

• Find the factors of 18
• 1 goes into 18, 18 times.
• 2 goes into 18, 9 times.
• 3 goes into 18, 6times.
• 4 does not divide 18 evenly.
• 5 does not divide 18 evenly.
• We are now back to 6. We have found all factors
  of 18.
• 1, 2, 3, 6 and 18

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Finding The GCF Using Factors

• Determine the greatest common factor of two
  numbers by finding all the factors for the two
  numbers then comparing them. The largest common
  factor of the two numbers is their greatest
  common factor.

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Using Factors

• Find the GCF of 36 and 24
• Factors of 36 1, 2, 3, 4, 6, 9, 12, 18 and 36
• Factors of 24 1, 2, 3, 4, 6, 8, 12 and 24
• The greatest common factor is of 36 and 24 is 12

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Using Factors Again

• Find the GCF of 15 and 100
• Factors of 15 1, 3, 5 and 15
• Factors of 100 1, 2, 4, 5, 10, 20, 25,
• 50 and 100
• The greatest common factor of 15 and 100 is 5

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Finding the Prime Factorization

• A prime factorization is when a product is broken
  down until only prime numbers remain. Prime
  numbers are numbers whos only factors and 1 and
  them self. A factor tree is useful in finding a
  prime factorization.

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Prime Factorization

• Break 18 down to only prime numbers.
• 18
• /\
• 9
• /\
• 3 3
• 18 2 2 3

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Finding the GCF Using Prime Factorization

• To determine the greatest common factor find the
  prime factorization for each number. Find all of
  the common prime factors of the two numbers and
  multiply them together. Your sum is the GCF.

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Using Prime Factorization

• Find the GCF of 36 and 24
• 36 24
• /\ /\
• 2 18 2 12
• /\ /\
• 2 9 2 6
• /\ /\
• 3 3 2 3
• 36 2233 24 2223
• The GCF of 36 and 24 is 22312

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Using Prime Factorization Again

• Find the GCF of 21 and 42
• 21 42
• /\ /\
• 3 7 2 21
• /\
• 3
  7
• 21 37 42 237
• The GCF of 21 and 42 is 37 21

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Greatest Common Factor

• Now you know how to find the greatest common
  factor you if you have any other questions check
  out these sites about finding the GCF
• Greatest Common Factor
• Free Math Help