Lesson 4.2 - Greatest Common Factor
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Five-Minute Check (over Lesson 4–1) Main Idea and Vocabulary Example 1:Find the Greatest Common Factor Example 2:Find the GCF of Three Numbers Example 3:Use the GCF to Solve a Problem Example 4:Use the GCF to Solve a Problem
• Find the greatest common factor of two or more numbers.
• Venn diagram • greatest common factor (GCF)
Find the Greatest Common Factor Find the GCF of 28 and 42. Method 1 List the factors of the numbers. factors of 28: 1, 2, 4, 7, 14, 28 factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 The common factors of 28 and 42 are 1, 2, 7, and 14. So, the GCF is 14.
Find the Greatest Common Factor Method 2 Use prime factorization. Write the prime factorization. Then circle the common factors. 28 = 2 ● 2 ● 7 42 = 2 ● 3 ● 7 The greatest common factor or GCF is 2 ● 7 or 14. Answer: 14
Find the Greatest Common Factor Method 3 Chinese Math. Write the two numbers side by side. Look for a common factor. Divide both numbers by that common factor. Look for a common factor between the two quotients, repeat until there are no more common factors. 7
28
42
2
14
6
7 is a common factor divide both numbers by 7. 2 is a common factor divide both numbers by 2.
7 3 The GCF is the product of the common factors. The greatest common factor or GCF is 2 ● 7 or 14. Answer: 14
Find the GCF of 18 and 45. B. 9
0% D
A B C 0% D C
0% B
A
0%
1. 2. 3. 4.
Find the GCF of Three Numbers Find the GCF of 21, 42, and 63. Method 1 List the factors of the numbers. factors of 21: 1, 3, 7, 21 factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 factors of 63: 1, 3, 7, 9, 21, 63 The greatest common factor or GCF is 21.
Find the GCF of Three Numbers Method 2 Use prime factorization. 21 =
3×7
42 = 2 × 3 × 7
Circle the common factors.
63 = 3 × 3 × 7 The common prime factors are 3 and 7. Answer: The GCF is 3 × 7, or 21.
Find the GCF of 24, 48, and 60. D. 12
0% D
A B C 0% D C
0% B
A
0%
1. 2. 3. 4.
ART Searra wants to cut a 15-centimeter by 25-centimeter piece of tag board into squares for an art project. She does not want to waste any of the tag board and she wants the largest squares possible. What is the length of the side of the squares she should use? The largest length of side possible is the GCF of the dimensions of the tag board. 15 = 3 × 5
The GCF of 15 and 25 is 5.
25 = 5 × 5 Answer: Searra should use squares with sides measuring 5 centimeters.
CANDY Alice is making candy baskets using chocolate hearts and lollipops. She is tying each piece of candy with either a red piece of string or a green piece of string. She has 64 inches of red string and 56 inches of green string. She wants to cut the pieces of string in equal length and use all of the string she has. What is the length of the longest piece of string that can be cut? C. 8 inches
1. 2. 3. 4.
0% D
0% C
0% B
A
0%
A B C D
ART Searra wants to cut a 15-centimeter by 25-centimeter piece of tag board into squares for an art project. She does not want to waste any of the tag board and she wants the largest squares possible. How many squares can she make if the sides are 5 centimeters? 25 ÷ 5 = 5 squares can fit along the length. 15 ÷ 5 = 3 squares can fit along the width. So, 5 × 3 = 15 squares can be made from the tag board. Answer: 15 squares
CANDY Alice is making candy baskets using chocolate hearts and lollipops. She is tying each piece of candy with either a red piece of string or a green piece of string. She has 64 inches of red string and 56 inches of green string. She wants to cut the pieces of string in equal length and use all of the string she has. How many pieces of string can be cut if the pieces are 8 inches long? B. 15 pieces
1. 2. 3. 4.
0% D
0% C
0% B
A
0%
A B C D
End of the Lesson
Homework - Pg 188-189, # 9-20, 22-36 EVEN
Five-Minute Check (over Lesson 4–1) Image Bank Math Tools
Percents Prime Factorization
(over Lesson 4-1)
Determine whether 47 is prime or composite. A. prime B. composite
A
0%
A B
0% B
1. 2.
(over Lesson 4-1)
Determine whether 63 is prime or composite. A. prime B. composite
0% D
A B C 0% D C
0% B
A
0%
1. 2. 3. 4.
(over Lesson 4-1)
Find the prime factorization of 54. A. 23 × 32 B. 22 × 33
A B C 0% D
0% D
A
D. 23 × 3
0% B
0%
1. 2. 3. 4.
C
C. 2 × 33
(over Lesson 4-1)
Find the prime factorization of 32. A. 22 × 32 B. 25
A B C 0% D
0% D
0% B
D. 24
A
0%
1. 2. 3. 4.
C
C. 23 × 2
(over Lesson 4-1)
Evaluate 2p2 + 5 for p = 0, 1, 2, 3. List the resulting numbers that are prime numbers. A. The resulting numbers 5, 7, 9, and 11 are all prime. B. The resulting numbers 5, 7, and 11 are all prime. A B C 0% D
0% D
0% B
A
D. The resulting numbers 5, 7, 13, and 23 are all prime.
0%
1. 2. 3. 4.
C
C. The resulting numbers 5, 7, 13, and 19 are all prime.
(over Lesson 4-1)
Zoran needs to rent storage space to store his furniture. He thinks he will need a floor space of 9 feet × 12 feet. What is the prime factorization of this area? A. 32 × 22 B. 33 × 22
1. 2. 3. 4.
C. 32 × 23 0% D
0% C
0% B
D. 33 × 23
A
0%
A B C D
• Find the greatest common factor of two or more numbers.
• Venn diagram • greatest common factor (GCF)
Find the Greatest Common Factor Find the GCF of 28 and 42. Method 1 List the factors of the numbers. factors of 28: 1, 2, 4, 7, 14, 28 factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 The common factors of 28 and 42 are 1, 2, 7, and 14. So, the GCF is 14.
Find the Greatest Common Factor Method 2 Use prime factorization. Write the prime factorization. Then circle the common factors. 28 = 2 ● 2 ● 7 42 = 2 ● 3 ● 7 The greatest common factor or GCF is 2 ● 7 or 14. Answer: 14
Find the Greatest Common Factor Method 3 Chinese Math. Write the two numbers side by side. Look for a common factor. Divide both numbers by that common factor. Look for a common factor between the two quotients, repeat until there are no more common factors. 7
28
42
2
14
6
7 is a common factor divide both numbers by 7. 2 is a common factor divide both numbers by 2.
7 3 The GCF is the product of the common factors. The greatest common factor or GCF is 2 ● 7 or 14. Answer: 14
Find the GCF of 18 and 45. B. 9
0% D
A B C 0% D C
0% B
A
0%
1. 2. 3. 4.
Find the GCF of Three Numbers Find the GCF of 21, 42, and 63. Method 1 List the factors of the numbers. factors of 21: 1, 3, 7, 21 factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 factors of 63: 1, 3, 7, 9, 21, 63 The greatest common factor or GCF is 21.
Find the GCF of Three Numbers Method 2 Use prime factorization. 21 =
3×7
42 = 2 × 3 × 7
Circle the common factors.
63 = 3 × 3 × 7 The common prime factors are 3 and 7. Answer: The GCF is 3 × 7, or 21.
Find the GCF of 24, 48, and 60. D. 12
0% D
A B C 0% D C
0% B
A
0%
1. 2. 3. 4.
ART Searra wants to cut a 15-centimeter by 25-centimeter piece of tag board into squares for an art project. She does not want to waste any of the tag board and she wants the largest squares possible. What is the length of the side of the squares she should use? The largest length of side possible is the GCF of the dimensions of the tag board. 15 = 3 × 5
The GCF of 15 and 25 is 5.
25 = 5 × 5 Answer: Searra should use squares with sides measuring 5 centimeters.
CANDY Alice is making candy baskets using chocolate hearts and lollipops. She is tying each piece of candy with either a red piece of string or a green piece of string. She has 64 inches of red string and 56 inches of green string. She wants to cut the pieces of string in equal length and use all of the string she has. What is the length of the longest piece of string that can be cut? C. 8 inches
1. 2. 3. 4.
0% D
0% C
0% B
A
0%
A B C D
ART Searra wants to cut a 15-centimeter by 25-centimeter piece of tag board into squares for an art project. She does not want to waste any of the tag board and she wants the largest squares possible. How many squares can she make if the sides are 5 centimeters? 25 ÷ 5 = 5 squares can fit along the length. 15 ÷ 5 = 3 squares can fit along the width. So, 5 × 3 = 15 squares can be made from the tag board. Answer: 15 squares
CANDY Alice is making candy baskets using chocolate hearts and lollipops. She is tying each piece of candy with either a red piece of string or a green piece of string. She has 64 inches of red string and 56 inches of green string. She wants to cut the pieces of string in equal length and use all of the string she has. How many pieces of string can be cut if the pieces are 8 inches long? B. 15 pieces
1. 2. 3. 4.
0% D
0% C
0% B
A
0%
A B C D
End of the Lesson
Homework - Pg 188-189, # 9-20, 22-36 EVEN
Five-Minute Check (over Lesson 4–1) Image Bank Math Tools
Percents Prime Factorization
(over Lesson 4-1)
Determine whether 47 is prime or composite. A. prime B. composite
A
0%
A B
0% B
1. 2.
(over Lesson 4-1)
Determine whether 63 is prime or composite. A. prime B. composite
0% D
A B C 0% D C
0% B
A
0%
1. 2. 3. 4.
(over Lesson 4-1)
Find the prime factorization of 54. A. 23 × 32 B. 22 × 33
A B C 0% D
0% D
A
D. 23 × 3
0% B
0%
1. 2. 3. 4.
C
C. 2 × 33
(over Lesson 4-1)
Find the prime factorization of 32. A. 22 × 32 B. 25
A B C 0% D
0% D
0% B
D. 24
A
0%
1. 2. 3. 4.
C
C. 23 × 2
(over Lesson 4-1)
Evaluate 2p2 + 5 for p = 0, 1, 2, 3. List the resulting numbers that are prime numbers. A. The resulting numbers 5, 7, 9, and 11 are all prime. B. The resulting numbers 5, 7, and 11 are all prime. A B C 0% D
0% D
0% B
A
D. The resulting numbers 5, 7, 13, and 23 are all prime.
0%
1. 2. 3. 4.
C
C. The resulting numbers 5, 7, 13, and 19 are all prime.
(over Lesson 4-1)
Zoran needs to rent storage space to store his furniture. He thinks he will need a floor space of 9 feet × 12 feet. What is the prime factorization of this area? A. 32 × 22 B. 33 × 22
1. 2. 3. 4.
C. 32 × 23 0% D
0% C
0% B
D. 33 × 23
A
0%
A B C D
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