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Activity 3 The Greatest Common Factor
jOb ective Learn about the greatest common factor.
CMath Vo abulary greatest common factor (GCF): the largest common factor of two or more numbers
1. Textbook Instructions Activity 3 The Greatest Common Factor
Tell the students about the greatest common Learn about the greatest common factor.
factor. Have the students practice finding the
greatest common factor by solving the given The greatest common factor (GCF) is the largest common factor of
problems. two or more numbers.
1. Have students find the factors and 1 . Find the greatest common factor.
common factors of two numbers and then
find the greatest common factor. Have them a. 4 and 18 b. 8 and 16
be careful not to miss any factors when
finding the factors of two numbers. Factors of 4: 1, 2, 4 Factors of 8: 1, 2, 4, 8
Example: 1a. Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 16: 1, 2, 4, 8, 16
4 1 4 2 2, so the factors of 4 are 1, 2, Common factors: 1, 2 Common factors: 1, 2, 4, 8
and 4. The greatest common factor: 2 The greatest common factor: 8
18 1 18 2 9 3 6, so the factors of
18 are 1, 2, 3, 6, 9, and 18. c. 12 and 15 d. 15 and 20
The common factors are 1 and 2, and the
greatest common factor is 2. Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 15: 1, 3, 5, 15
Factors of 15: 1, 3, 5, 15 Factors of 20: 1, 2, 4, 5, 10, 20
Common factors: 1, 3 Common factors: 1, 5
The greatest common factor: 3 The greatest common factor: 5
2. Have students solve the problems using 2 . Solve each word problem using the greatest common factor.
the problem solving method. a. There are 12 oranges and 18 apples. Thomas wants to put an equal
number of oranges and apples in each box. What is the greatest number
Refer to . of boxes that he needs? 6 boxes
b. Jessica wants to give an equal number of pencils and erasers to her
friends. If there are 24 pencils and 36 erasers, what is the greatest
number of friends that she can give them? 12 friends
16
2. Build Understanding
Problem Solving Method Plan the Process Solve the Problem
Q: How will you solve the problem? Factors of 12: 1, 2, 3, 4, 6, 12.
Example: 2a. A: Find the common factors and then Factors of 18: 1, 2, 3, 6, 9, 18.
Understand the Question Common factors: 1, 2, 3, 6.
Q: What do you need to find? find the greatest common factor of The greatest common factor: 6
A: What is the greatest number of boxes two numbers. The answer is 6 boxes.
that he needs? Look Back
Q: Read the problem again. What do Q: Does your answer make sense?
you already know?
A: There are 12 oranges and 18 apples.
Thomas wants to put an equal
number of oranges and apples in
each box.
024 NUMINO Teacher s Guide
jOb ective Learn about the greatest common factor.
CMath Vo abulary greatest common factor (GCF): the largest common factor of two or more numbers
1. Textbook Instructions Activity 3 The Greatest Common Factor
Tell the students about the greatest common Learn about the greatest common factor.
factor. Have the students practice finding the
greatest common factor by solving the given The greatest common factor (GCF) is the largest common factor of
problems. two or more numbers.
1. Have students find the factors and 1 . Find the greatest common factor.
common factors of two numbers and then
find the greatest common factor. Have them a. 4 and 18 b. 8 and 16
be careful not to miss any factors when
finding the factors of two numbers. Factors of 4: 1, 2, 4 Factors of 8: 1, 2, 4, 8
Example: 1a. Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 16: 1, 2, 4, 8, 16
4 1 4 2 2, so the factors of 4 are 1, 2, Common factors: 1, 2 Common factors: 1, 2, 4, 8
and 4. The greatest common factor: 2 The greatest common factor: 8
18 1 18 2 9 3 6, so the factors of
18 are 1, 2, 3, 6, 9, and 18. c. 12 and 15 d. 15 and 20
The common factors are 1 and 2, and the
greatest common factor is 2. Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 15: 1, 3, 5, 15
Factors of 15: 1, 3, 5, 15 Factors of 20: 1, 2, 4, 5, 10, 20
Common factors: 1, 3 Common factors: 1, 5
The greatest common factor: 3 The greatest common factor: 5
2. Have students solve the problems using 2 . Solve each word problem using the greatest common factor.
the problem solving method. a. There are 12 oranges and 18 apples. Thomas wants to put an equal
number of oranges and apples in each box. What is the greatest number
Refer to . of boxes that he needs? 6 boxes
b. Jessica wants to give an equal number of pencils and erasers to her
friends. If there are 24 pencils and 36 erasers, what is the greatest
number of friends that she can give them? 12 friends
16
2. Build Understanding
Problem Solving Method Plan the Process Solve the Problem
Q: How will you solve the problem? Factors of 12: 1, 2, 3, 4, 6, 12.
Example: 2a. A: Find the common factors and then Factors of 18: 1, 2, 3, 6, 9, 18.
Understand the Question Common factors: 1, 2, 3, 6.
Q: What do you need to find? find the greatest common factor of The greatest common factor: 6
A: What is the greatest number of boxes two numbers. The answer is 6 boxes.
that he needs? Look Back
Q: Read the problem again. What do Q: Does your answer make sense?
you already know?
A: There are 12 oranges and 18 apples.
Thomas wants to put an equal
number of oranges and apples in
each box.
024 NUMINO Teacher s Guide
