# 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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