Transcript 4.3 Greatest Common Factors (GCF)

4.3 Greatest Common Factors
(GCF)
I can find the greatest common
factor of a set of numbers
Review
A factor is number that is multiplied by
another number to get a product
A prime number is a number that can
only be divided by only one and itself.
A composite number is a number
greater than one that is not prime.
Prime or composite?
37
prime
51
composite
The greatest common factor is the
largest factor that two or more numbers
share.
Factors of 24:
Factors of 36:
1, 2, 3, 4, 6, 8, 12, 24
1, 2, 3, 4, 6, 9, 12, 18, 36
Common factors: 1, 2, 3, 4, 6, 12
The greatest common factor (GCF) of 24 and 36
is 12.
Example 1 shows three different methods for
finding the GCF.
Additional Example 1A: Finding the GCF
Find the GCF of the set of numbers.
28 and 42
Method 1: List the factors.
factors of 28: 1, 2, 4, 7, 14, 28
List all the factors.
factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Circle the GCF.
The GCF of 28 and 42 is 14.
Additional Example 1B: Finding the GCF
Find the GCF of the set of numbers.
18, 30, and 24
Method 2: Use the prime factorization.
18 = 2 • 3 • 3
30 = 2 • 3 • 5
24 = 2 • 3 • 2 • 2
2•3= 6
Write the prime factorization of each
number.
Find the common prime factors.
Find the prime factors common to
all the numbers.
The GCF of 18, 30, and 24 is 6.
Additional Example 1C: Finding the GCF
Find the GCF of the set of numbers.
45, 18, and 27
Method 3: Use a ladder diagram.
3
45 18 27
3 15 6 9
5 2 3
3•3= 9
Begin with a factor that divides into
each number. Keep dividing until the
three have no common factors.
Find the product of the numbers
you divided by.
The GCF of 45, 18, and 27 is 9.
Check It Out: Example 1A
Find the GCF of the set of numbers.
18 and 36
Method 1: List the factors.
factors of 18: 1, 2, 3, 6, 9, 18
List all the factors.
factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 Circle the GCF.
The GCF of 18 and 36 is 18.
Check It Out: Example 1B
Find the GCF of the set of numbers.
10, 20, and 30
Method 2: Use the prime factorization.
10 = 2 • 5
20 = 2 • 5 • 2
30 = 2 • 5 • 3
2 • 5 = 10
Write the prime factorization of each
number.
Find the common prime factors.
Find the prime factors common to
all the numbers.
The GCF of 10, 20, and 30 is 10.
Check It Out: Example 1C
Find the GCF of the set of numbers.
40, 16, and 24
Method 3: Use a ladder diagram.
2
Begin with a factor that divides into
40 16 24
each number. Keep dividing until the
2 20 8 12
three have no common factors.
2 10 4 6
5 2 3
2 • 2 • 2 =8
Find the product of the numbers
you divided by.
The GCF of 40, 16, and 24 is 8.
Additional Example 2: Problem Solving Application
Jenna has 16 red flowers and 24 yellow
flowers. She wants to make bouquets with
the same number of each color flower in
each bouquet. What is the greatest
number of bouquets she can make?
1
Understand the Problem
The answer will be the greatest number of
bouquets 16 red flowers and 24 yellow
flowers can form so that each bouquet has
the same number of red flowers, and each
bouquet has the same number of yellow
flowers.
2 Make a Plan
You can make an organized list of the
possible bouquets.
3
Solve
Red Yellow
2
3
Bouquets
RR
RR
RR
RR
RR
RR
RR
RR
YYY
YYY
YYY
YYY
YYY
YYY
YYY
YYY
16 red, 24 yellow:
Every flower is in a bouquet
The greatest number of bouquets Jenna can make is 8.
4 Look Back
To form the largest number of bouquets, find the GCF of 16
and 24. factors of 16: 1, 2, 4, 8, 16
factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The GCF of 16 and 24 is 8.
Lesson Quiz: Part II
Find the greatest common factor of the
set of numbers.
5. Mrs. Lovejoy makes flower arrangements. She
has 36 red carnations, 60 white carnations,
and 72 pink carnations. Each arrangement
must have the same number of each color.
What is the greatest number of arrangements
she can make if every carnation is used?
12 arrangements