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The G.C.F.

The G.C.F. Definitions. A common factor is a factor that two or more numbers share. The gcf , or greatest common factor of a set of numbers is the greatest common factor. Two or more numbers are relatively prime if the gcf between them is 1. Method #1.

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The G.C.F.

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  1. The G.C.F.

  2. Definitions A common factor is a factor that two or more numbers share. The gcf, or greatest common factor of a set of numbers is the greatest common factor. Two or more numbers are relatively prime if the gcf between them is 1.

  3. Method #1 Find the greatest common factor of the numbers by listing factors. 1. 16, 28 2. 60, 96 3. 14, 70, 91

  4. Another Example An orchestra conductor divides 48 violinists, 24 violists, and 36 cellists into ensembles. Each ensemble has the same number of each instrument. What is the greatest number of ensembles that can be formed? How many violinists, violists, and cellists will be in each ensemble?

  5. Method #2 Using Prime Factorization to Find the GCF Step #1: Begin by writing the prime factorization of each number. Step #2: Circle the common factors. Step #3: The GCF is the product of all of the common factors.

  6. Find the greatest common factor of 180 and 126 using prime factorization.

  7. Find the greatest common factor of the numbers using prime factorization. 90, 150 84, 216

  8. Another Example What is the greatest number of ensembles that can be formed with 32 violinists, 40 violists, and 16 cellists? How many of each instrument will be in each ensemble?

  9. Tell whether the numbers are relatively prime. 13, 24 16, 25

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