Transcript greatest common factor

Greatest Common Factor
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
Greatest Common Factor
Warm Up
Write the prime factorization of each
number.
1. 14
27
2. 63
3 x 3 x 7 = 32  7
3. 18
2 x 3 x 3 = 2  32
Greatest Common Factor
Learn to find the greatest common factor
(GCF) of a set of numbers.
Greatest Common Factor
Vocabulary
greatest common factor (GCF)
Greatest Common Factor
Factors shared by two or more whole numbers
are called common factors. The largest of the
common factors is called the greatest
common factor, or GCF.
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.
Greatest Common Factor
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.
Greatest Common Factor
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.
Greatest Common Factor
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.
Greatest Common Factor
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.
Greatest Common Factor
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.
Greatest Common Factor
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.
Greatest Common Factor
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?
Greatest Common Factor
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.
Greatest Common Factor
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.
Greatest Common Factor
Check It Out: Example 2
Peter has 18 oranges and 27 pears. He
wants to make fruit baskets with the
same number of each fruit in each
basket. What is the greatest number of
fruit baskets he can make?
Greatest Common Factor
Check It Out: Example 2 Continued
1
Understand the Problem
The answer will be the greatest number of
fruit baskets 18 oranges and 27 pears can
form so that each basket has the same
number of oranges, and each basket has
the same number of pears.
2
Make a Plan
You can make an organized list of the
possible fruit baskets.
Greatest Common Factor
3
Solve
Oranges
Pears
2
3
Bouquets
OO
OO
OO
OO
OO
OO
OO
OO
OO
PPP
PPP
PPP
PPP
PPP
PPP
PPP
PPP
PPP
18 oranges, 27 pears:
Every fruit is in a basket
The greatest number of baskets Peter can make is 9.
4
Look Back
To form the largest number of baskets, find the GCF of 18 and
1, 2, 3, 6, 9, 18
27. factors of 18:
factors of 27: 1, 3, 9, 27
The GCF of 18 and 27 is 9.
Greatest Common Factor
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
Greatest Common Factor
Lesson Quiz: Part I
Find the greatest common factor of each
set of numbers.
1. 18 and 30
6
2. 20 and 35
5
3. 8, 28, 52
4
4. 44, 66, 88
22
Greatest Common Factor
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
Greatest Common Factor
Lesson Quiz for Student Response Systems
1. Identify the greatest common factor of 28
and 36.
A. 2
B. 4
C. 6
D. 7
Greatest Common Factor
Lesson Quiz for Student Response Systems
2. Identify the greatest common factor of 49
and 77.
A. 3
B. 5
C. 7
D. 11
Greatest Common Factor
Lesson Quiz for Student Response Systems
3. Identify the greatest common factor of 16,
24, and 40.
A. 2
B. 4
C. 5
D. 8
Greatest Common Factor
Lesson Quiz for Student Response Systems
4. Identify the greatest common factor of 42,
63, and 84.
A. 3
B. 7
C. 19
D. 21
Greatest Common Factor
Lesson Quiz for Student Response Systems
5. Harry collected 42 first-aid kits, 56
blankets, and 70 food packets for a floodrelief camp. He wants to pack the collected
items in boxes in such a way that each box
has the same number of items of each kind.
What is the greatest number of boxes that
Harry needs?
A. 7 boxes
B. 14 boxes
C. 21 boxes
D. 24 boxes