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Mathematics: Applications and Concepts, Course 2 Interactive Chalkboard
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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 12p2 and 30p3.
Factor each expression.
Circle the common factors.
Answer: The GCF is 2
ALGEBRA Find the GCF of
Answer: 7mn
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
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