4.3 Greatest Common Factors (GCF)

1
4.3 Greatest Common Factors (GCF)

• I can find the greatest common factor of a set of
  numbers

2
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

3
The greatest common factor is the largest factor
that two or more numbers share.
Factors of 24 Factors of 36 Common factors
1,
2,
3,
4,
6,
8,
12,
24
1,
2,
3,
4,
6,
9,
12,
18,
36
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.
4
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 factors of 42
List all the factors.
1,
2,
14,
7,
28
4,
7,
1,
3,
2,
42
6,
21,
14,
Circle the GCF.
The GCF of 28 and 42 is 14.
5
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 30 24
2
3
3
Write the prime factorization of each number.


5

2
3

2
2
2
3



Find the common prime factors.
Find the prime factors common to all the numbers.
2 3
6
The GCF of 18, 30, and 24 is 6.
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
Begin with a factor that divides into each
number. Keep dividing until the three have no
common factors.
3
5 2 3
Find the product of the numbers you divided by.
3 3
9
The GCF of 45, 18, and 27 is 9.
7
Check It Out Example 1A Find the GCF of the set
of numbers.
18 and 36 Method 1 List the factors. factors of
18 factors of 36
List all the factors.
1,
2,
9,
6,
18
3,
6,
1,
3,
2,
36
4,
12,
9,
Circle the GCF.
18,
The GCF of 18 and 36 is 18.
8
Check It Out Example 1B Find the GCF of the set
of numbers.
10, 20, and 30 Method 2 Use the prime
factorization. 10 20 30
2
5
Write the prime factorization of each number.

2

2
5

3
2
5


Find the common prime factors.
Find the prime factors common to all the numbers.
2 5
10
The GCF of 10, 20, and 30 is 10.
9
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 each
number. Keep dividing until the three have no
common factors.
2
2
5 2 3
Find the product of the numbers you divided by.
2 2 2
8
The GCF of 40, 16, and 24 is 8.
10
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?
11
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.
You can make an organized list of the possible
bouquets.
12
16 red, 24 yellow Every flower is in a bouquet
The greatest number of bouquets Jenna can make is
8.
Look Back
To form the largest number of bouquets, find the
GCF of 16 and 24. factors of 16 factors of 24
1,
8,
4,
2,
16
1,
3,
24
8,
2,
4,
6,
12,
The GCF of 16 and 24 is 8.
13
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