Transcript Interactive Chalkboard - Warren County Public Schools
Mathematics: Applications and Concepts, Course 2 Interactive Chalkboard
Copyright © by The McGraw-Hill Companies, Inc.
Developed by FSCreations, Inc., Cincinnati, Ohio 45202
Send all inquiries to:
GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240
Lesson 5-1 Prime Factorization
Lesson 5-2 Greatest Common Factor
Lesson 5-7 Least Common Multiple
Example 1 Identify Numbers as Prime or Composite
Example 2 Identify Numbers as Prime or Composite
Example 3 Find the Prime Factorization
Example 4 Factor an Algebraic Expression
Determine whether the number 63 is prime or composite.
Answer:
The number 63 has six factors: 1, 3, 7, 9, 21, and 63. So, it is composite.
Determine whether the number 41 is prime or composite.
Answer:
prime
Determine whether the number 29 is prime or composite.
Answer:
The number 29 has only two factors, 1 and 29, so it is prime.
Determine whether the number 24 is prime or composite.
Answer:
composite
Find the prime factorization of 100.
Method 1
Use a factor tree.
Method 2
Divide by prime numbers.
Start here.
Answer:
The prime factorization of 100 is
Find the prime factorization of 72.
Answer:
ALGEBRA Factor Answer:
ALGEBRA Factor Answer:
Example 1 Find the GCF by Listing Factors
Example 2 Find the GCF Using Prime Factors
Example 3 Find the GCF Using Prime Factors
Example 4 Find the GCF of an Algebraic Expression
Example 5 Use the GCF to Solve a Problem
Find the GCF of 28 and 42.
First, list the factors of 28 and 42.
factors of 28: 1 , 2 , 4, 7 , 14 , 28 factors of 42: 1 , 2 , 3, 6, 7 , 14 , 21, 42 Notice that 1, 2, 7, and 14 are common factors of 28 and 42. So, the GCF is 14.
Check
You can draw a Venn diagram to check your answer.
Answer:
14
Find the GCF of 18 and 45.
Answer:
9
Find the GCF of 20 and 32.
Method 1
Write the prime factorization.
The common prime factors are 2 and 2.
Method 2
Divide by prime numbers.
Divide both 20 and 32 by 2. Then divide the quotients by 2.
Start here.
Answer:
The GCF of 20 and
Find the GCF of 24 and 36.
Answer:
12
Find the GCF of 21, 42, and 63.
Circle the common factors.
The common prime factors are 3 and 7.
Answer:
The GCF is 3 7, or 21.
Find the GCF of 24, 48, and 60.
Answer:
12
ALGEBRA Find the GCF of 12p 2 and 30p 3 .
Factor each expression.
Circle the common factors.
Answer:
The GCF is 2
ALGEBRA Find the GCF of Answer:
7
mn
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.
The GCF of 15 and 25 is 5.
Answer:
Searra should use squares with sides measuring 5 centimeters.
CANDY Alice is making candy baskets using chocolate hearts and lollipops. She has 32 chocolate hearts and 48 lollipops. She wants to have an equal number of chocolate hearts and lollipops in each basket. Find the greatest number of chocolate hearts and lollipops Alice can put in each basket.
Answer:
16
Example 1 Find the LCM by Listing Multiples
Example 2 Find the LCM Using Prime Factors
Example 3 Find the LCM by Using Prime Factors
Find the LCM of 4 and 6.
First, list the multiples of 4 and 6.
multiples of 4: 4, 8, 12 , 16, 20, 24 , 28, 32, 36 . . .
multiples of 6: 6, 12 , 18, 24 , 30, 36, . . .
Notice that 12, 24, . . ., are common multiples.
Answer:
The LCM of 4 and 6 is 12.
Find the LCM of 8 and 12.
Answer:
24
Find the LCM of 4 and 15.
Write the prime factorization.
The prime factors of 4 and 15 are 2, 3, and 5. Multiply the greatest power of 2, 3, and 5.
Answer:
The LCM of 4 and 15 is 60.
Find the LCM of 6 and 14.
Answer:
42
Find the LCM of 18, 24, and 48.
LCM:
Answer:
The LCM of 18, 24, and 48 is 144.
Find the LCM of 12, 20, and 45.
Answer:
180
Explore online information about the information introduced in this chapter.
Click on the
Connect
button to launch your browser and go to the
Mathematics: Applications and Concepts, Course 2
Web site. At this site, you will find extra examples for each lesson in the Student Edition of your textbook. When you finish exploring, exit the browser program to return to this presentation. If you experience difficulty connecting to the Web site, manually launch your Web browser and go to
www.msmath2.net/extra_examples
.
Click the mouse button or press the Space Bar to display the answers.
Click the mouse button or press the Space Bar to display the answers.
Click the mouse button or press the Space Bar to display the answers.
Click the mouse button or press the Space Bar to display the answers.
End of Custom Shows WARNING! Do Not Remove
This slide is intentionally blank and is set to auto-advance to end custom shows and return to the main presentation.