1. Greatest Common Factor
Lesson 4.2

2. Greatest Common Factor
Greatest common factor (GCF) – the greatest (largest) factor that two or more numbers have in common

3. Greatest Common Factor
A Venn diagram or list can be created to find the GCF of a set of numbers.
Example 1 – Find the GCF of 24 and 54 by making a list.
Factors of 24
Factors of 54
1, 24
1, 54
2, 12
2, 27
3, 8
3, 18
4, 6
6, 9

4. Your Turn Question #1 – Find the GCF of 32 and 48. Factors of 32
1, 32
1, 48
2, 16
2, 24
4, 8
3, 16
4, 12
6, 8

5. Your Turn Question #2 – Find the GCF of 35 and 56. Factors of 35
1, 32
1, 56
5, 7
2, 28
4, 14
7, 8

6. Greatest Common Factor
Example 2 Find the GCF of 24 and 40 by making a Venn diagram.
Common Factors
Factors of 24
Factors of 40 5 1 10 3 2 4 6 12 20 8 24 40

7. Your Turn
Quesiton #3 – Find the GCF of 18 and 60 by making a Venn diagram.
Common Factors
Factors of 18
Factors of 60 4 18 1 9 5 2 3 10 12 6 15 20 30 60
GCF: 6

8. Your Turn Question #4 – Find the GCF of 24, 56 and 80. Factors of 24
1, 24
1, 48
1, 80
2, 12
2, 28
2, 40
3, 8
4, 14
4, 20
4, 6
6, 8
5, 16
8, 10

9. Greatest Common Factor
Example 3 – Find the GCF of 30 and 42 using prime factorization. 30 42 3 x 10 2 x 21 3 x 2 x 5 2 x 3 x 7 3 x 2 = 6
GCF: 6

10. Your Turn
Question #5 – Find the GCF of 45 and 54 using prime factorization. 45 54 3 x 15 2 x 27 3 x 3 x 5 2 x 3 x 9 2 x 3 x 3 x 3 3 x 3 = 9
GCF: 9

11. Your Turn
Question #6 – Three classes of students are participating in a basketball tournament. There are 12, 18, and 27 students in each class. The students will be divided into equal teams with the same number of players on each team. Find the greatest number of people that can play on each team.
Factors of 12
Factors of 18
Factors of 27
1, 12
1, 18
1, 27
2, 6
2, 9
3, 9
3, 4
3, 6
The greatest number of people that can play on each team is 3.

12. Homework Assignment PRACTICE PROBLEMS
Pages 166 #12, 16, 17, 18, 28 (USA)

13. Sunshine State Standards (http://www. floridastandards
MA.7.A.3.2 – Add, subtract, multiply, and divide integers, fractions, and terminating decimals, and perform exponential operations with rational bases and whole number exponents including solving problems in everyday contexts.