Download a pair of numbers with no common factors except for 1

PT 3.3.2
August 31, 2016
Problem 3.3
Using Prime Factorizations
Focus Question: How can the prime factorization of
a number be used to find the LCM and GCF of two or
more numbers?
Vocabulary
relatively prime numbers
a pair of numbers with no common
factors except for 1
PT 3.3.2
August 31, 2016
What are the common factors of 24 and 60?
Greatest Common Factor (GCF)?
24 - 1, 2, 3, 4, 6, 8, 12, 24
60 - 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
GCF - 12
What are some common multiples of 24 and 60?
Least Common Multiple (LCM)?
24 - 24, 48, 72, 96, 120, 144, 168, 192...
60 - 60, 120, 180, 240, 300...
LCM - 120
Using Lists
1. List the factors of each
number.
2. Circle the factors that are
on both lists.
3. The largest circled factor is
the GCF.
GCF
Example:
GCF of 24 and 60
24: 1, 2, 3, 4, 6, 8, 12, 24
60: 1, 2, 3, 4, 5, 6, 10, 12, 15,
20, 30, 60
GCF = 12
1. List the multiples of each
number.
2. Circle the multiples that are
on both lists.
LCM
3. The smallest circled
multiple is the LCM.
Example:
LCM of 24 and 60
24: 24, 48, 72, 96, 120, 144...
60: 60, 120, 180, 240...
LCM = 120
Prime Factorization
Venn Diagram &
Prime Factorization
PT 3.3.2
August 31, 2016
Use the prime factorizations for 24 and 60 to find the
Greatest Common Factor.
24 = 2 x 2 x 2 x 3
60 =
2x2x3x5
Use the prime factorizations for 24 and 60 to find the
Least Common Multiple.
24 = 2 x 2 x 2 x 3
60 =
2x2x3x5
PT 3.3.2
August 31, 2016
Using Lists
Prime Factorization
1. List the factors of each
number.
2. Circle the factors that are
on both lists.
Venn Diagram &
Prime Factorization
1. Find the prime factorization
of both numbers.
2. The GCF is the product of all
the numbers that are in
3. The largest circled factor is common in the prime
the GCF.
factorization.
GCF
Example:
GCF of 24 and 60
24: 1, 2, 3, 4, 6, 8, 12, 24
60: 1, 2, 3, 4, 5, 6, 10, 12, 15,
20, 30, 60
GCF = 12
1. List the multiples of each
number.
LCM
Example:
GCF of 24 and 60
24 = 2 x 2 x 2 x 3
60 =
2x2x3x5
GCF = 2 x 2 x 3 = 12
1. Find the prime factorization
of both numbers.
2. Circle the multiples that are 2. The LCM is the product of
on both lists.
the numbers that are in
common multiplied by all of
3. The smallest circled
the "leftovers".
multiple is the LCM.
Example:
LCM of 24 and 60
24: 24, 48, 72, 96, 120, 144...
60: 60, 120, 180, 240...
Example:
LCM of 24 and 60
24 = 2 x 2 x 2 x 3
60 =
2x2x3x5
LCM = 120
LCM = 2 x 2 x 2 x 3 x 5 = 120
GCF with Prime Factorization & Venn Diagram
24
60
PT 3.3.2
August 31, 2016
LCM with Prime Factorization & Venn Diagram
24
60
Using Lists
1. List the factors of each
number.
2. Circle the factors that are
on both lists.
Prime Factorization
1. Find the prime factorization
of both numbers.
2. The GCF is the product of all
the numbers that are in
3. The largest circled factor is common in the prime
the GCF.
factorization.
GCF
Example:
GCF of 24 and 60
24: 1, 2, 3, 4, 6, 8, 12, 24
60: 1, 2, 3, 4, 5, 6, 10, 12, 15,
20, 30, 60
GCF = 12
Example:
GCF of 24 and 60
24 = 2 x 2 x 2 x 3
60 =
2x2x3x5
GCF = 2 x 2 x 3 = 12
Venn Diagram &
Prime Factorization
1. Find the prime
factorization for both
numbers.
2. Fill in the Venn Diagram
with pieces of the prime
factorizations.
3. The GCF is the product of
all of the numbers in
common in the prime
factorization.
Example:
GCF of 24 and 60
2x2x2x3x5
GCF = 2 x 2 x 3 = 12
1. List the multiples of each
number.
LCM
1. Find the prime factorization
of both numbers.
2. Circle the multiples that are 2. The LCM is the product of
on both lists.
the numbers that are in
common multiplied by all of
3. The smallest circled
the "leftovers".
multiple is the LCM.
Example:
LCM of 24 and 60
24: 24, 48, 72, 96, 120, 144...
60: 60, 120, 180, 240...
Example:
LCM of 24 and 60
24 = 2 x 2 x 2 x 3
60 =
2x2x3x5
LCM = 120
LCM = 2 x 2 x 2 x 3 x 5 = 120
1. Find the prime
factorization for both
numbers.
2. Fill in the Venn Diagram
with pieces of the prime
factorizations.
3. The LCM is the product of
everything in the Venn
Diagram.
Example:
LCM of 24 and 60
2x2x2x3x5
LCM = 2 x 2 x 2 x 3 x 5 = 120
PT 3.3.2
August 31, 2016
Quiz FRIDAY on factorizations,
prime factorization, and
exponents
PT 3.3.2
August 31, 2016