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4-2 Greatest Common Factor
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
4-2 Greatest Common Factor
Warm UpWrite the prime factorization of each number.
1. 14 3. 63
2. 18 4. 54
2 7 32 7
2 32 2 33
4-2 Greatest Common Factor
Problem of the Day
In a parade, there are 15 riders on bicycles and tricycles. In all, there are 34 cycle wheels. How many bicycles and how many tricycles are in the parade?
11 bicycles and 4 tricycles
4-2 Greatest Common Factor
Learn to find the greatest common factor (GCF) of a set of numbers.
4-2 Greatest Common Factor
Vocabulary
greatest common factor (GCF)
4-2 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:
Common factors:
1, 2, 3, 4, 6, 8,
1, 2, 3, 4, 6,
The greatest common factor (GCF) of 24 and 36 is 12.
Example 1 shows three different methods for finding the GCF.
1, 2, 3, 4, 6, 9,
12,
12, 18,
24
36
12
4-2 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:
factors of 42:
1, 2, 14, 7, 28
7, 1,
4,
3, 2, 42 6, 21, 14,
List all the factors.
Circle the GCF.
The GCF of 28 and 42 is 14.
4-2 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 =
30 =
24 =
2
5 •
3
2
2
3
2
3
23
Write the prime factorization of each number.
Find the common prime factors.
The GCF of 18, 30, and 24 is 6.
•
•
•
•
•
•
Find the prime factors common to all the numbers.
2 • 3 = 6
4-2 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
3
5 2 3
45 18 27 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.
3 • 3 =
The GCF of 45, 18, and 27 is 9.
9
15 6 9
4-2 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:
factors of 36:
1, 2, 9, 6, 18
6, 1,
3,
3, 2, 36 4, 12, 9,
List all the factors.
Circle the GCF.
The GCF of 18 and 36 is 18.
18,
4-2 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 =
20 =
30 =
2
2 •
3
2
5
2
5
5
Write the prime factorization of each number.
Find the common prime factors.
The GCF of 10, 20, and 30 is 10.
•
•
•
•
Find the prime factors common to all the numbers.
2 • 5 = 10
4-2 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
2
40 16 24 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.
2 • 2 • 2 =
The GCF of 40, 16, and 24 is 8.
8
20 8 12
5 2 3 10 4 62
4-2 Greatest Common Factor
Check For Understanding
1. 18 and 30
2. 20 and 35
3. 8, 28, 52
4. 44, 66, 88
5
6
4
22
Find the greatest common factor of each set of numbers.
4-2 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
4-2 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
4-2 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
4-2 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
