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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  
2^{8}  2^{7} 
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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