6th Grade Math Textbook, Fundamentals

Method 1 Use Division

2,691 1,9891R702

1,989 702 2R585

702  585 1R117

585  117 5 R0

The GCF is 117.

Method 2 Use Subtraction

2,691 1,989  702

1,989  702 1,287

1,287  702  585

702  585  117

585  117  468

468  117  351

351  117  234

234  117  117

The GCF is 117.

144 Chapter 5

More Enrichment Topics

Use any method (or more than one) to find the GCF of these pairs of numbers.

1.21, 28 2.202, 2,002 3.17, 68 4.54, 180 5.45, 16

6.Discuss and Write For one of the problems, you found a GCF of 1.

What does that mean?

page 159 for exercise sets.

Enrichment:

Different Ways to Find the GCF

Objective To explore different algorithms for finding the greatest common factor (GCF) of two numbers

Finding the GCF of two numbers by listing factors can be time-consuming. Since the
time of ancient Greece, people have used other methods to find the GCF.

Look at these two ways to find the GCF of 10 and 18.

As you use these methods, you divide or subtract until you find the result

you want. These methods are iterative. An iterative process repeats over

and over.

Now use the two methods above to find the GCF of 1,989 and 2,691.

Method 1 Use Division

• Divide the greater number by the lesser
  number.


• If the remainder is 0, the lesser number
  is the GCF. If not, divide the divisor by
  the remainder.


• Continue this process until the remainder
  is 0. The last divisor is the GCF.
  18  10 1R8
  10  8 1R2
  8  2 4R0
  The GCF is 2.

Method 2 Use Subtraction

• Subtract the lesser number from the
  greater number.


• Then compare the three numbers (the two
  numbers and the difference) and subtract the
  least number from the next least number.


• Continue until two of the three numbers are
  the same. That number is the GCF.
  18  10  8
  10  8  2
  8  2  6
  6  2  4
  4  2  2
  The GCF is 2.