This document provides instruction on finding the greatest common factor (GCF) of multiple numbers. It begins with defining key terms like greatest, common, and factor. Students are asked to find the prime factorizations and GCF of various number pairs. The GCF is explained as the product of the smallest powers of each common factor between the numbers. Students will complete think-pair-share and practice problems finding GCFs using prime factorizations.

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Do Now
AIM: Greatest Common Factor

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Anticipatory Set
1.) Define Greatest.
2.) Define Common.
3.) Define Factor.
Greatest Common Factor

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1.) Based on methods you have used in previous math
classes, find the greatest common factor of the following
numbers.
24:
36:
2.) Explain the method you used to find the greatest
common factor.
Anticipatory Set:
1, 2, 3, 4, 6, 8, 12, 24
1, 2, 3, 4, 6, 9, 12, 18, 36

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3.) Find the Prime Factorizations of the following
numbers. Write the answer in exponential form.
24 36

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3.) Find the Prime Factorizations of the following
numbers. Write the answer in exponential form.
24 36
6 4 6 6
3 2 2 2 3 32 2

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3.) Find the Prime Factorizations of the following
numbers. Write the answer in exponential form.
24 36
6 4 6 6
3 2 2 2 3 32 2

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3.) Find the Prime Factorizations of the following
numbers. Write the answer in exponential form.
24 36
6 4 6 6
3 2 2 2 3 32 2
24 = 23
3
36 = 22
32

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3.) Find the Prime Factorizations of the following
numbers. Write the answer in exponential form.
24 36
6 4 6 6
3 2 2 2 3 32 2
24 = 23
3
36 = 22
32
Finding Greatest Common Factor: The product of the
smallest power of each common factor.

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Think-Pair-Share Activity:
Find the greatest common factor of the
following numbers using the prime factorizations
of the numbers.
1.) 40 56

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2.) 9 16

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3.) 84 54 144

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Extra Practice

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4.) The parents are making sandwiches for the class picnic. They have 72 turkey
slices, 48 cheese slices, and 96 tomato slices. What is the greatest number of
sandwiches they can make if each sandwich has the same filling? (Use the prime
factorizations of the numbers)

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5.) Two bicycle enthusiasts are leaving Cincinnati at the same
time. One is biking 840 miles to Boston. The other is biking
440 miles to Atlanta. What is the greatest number of miles a
day each can bike if they want to cover equal distances each
day?

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1.) Why is the Greatest Common Factor of several numbers
the “Greatest” when it is less than or equal to the numbers?
BEFORE YOU LEAVE:

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Homework: Pages 84-85 #11-13 all, 21-25 all, 38, 39, 41, 46-49 all
Mr. Tjersland's Math 7