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More with the GCF

Your Task: Consider the following statements:

Definition: The greatest common factor of two whole numbers a and b is the largest
number that is a factor of both a and b. We denote it by GCF (a, b).

Example: GCF (2, 8) = 2 because 2 = 2∙1 and 8 = 2∙4. There is no greater number that
satisfies that condition.

1. Find GCF (3, 12) using your own method . Explain your reasoning and how you
arrived at your answer. Please do not refer to your textbook at this time. If you are
stuck, I will help you!

2. Fill in the following table. Look for shortcuts!

a b a - b GCF (a, b) GCF (a – b, b)
12 3
3 2
125 10
1000 88
2348 2346
28 27

3. Make a conjecture based on the patterns present in this table . Are there any
restrictions on your conjecture?

4. Do you think your conjecture is true in all cases? If so, why? If not, why not?

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