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Greatest Common Factor (GCF)

- Greatest Common Factor: the largest factor that two numbers share.
- Factor: one of the numbers being multiplied

Two Ways To Determine GCF

- List all the factors and find the greatest common factor
- Prime factorization, find the common factors and multiply

12

42

1 ● 42

Factors of 12:

1, 2, 3, 4, 6,12

1 ● 12

2 ● 21

2 ● 6

3 ● 14

3 ● 4

4 ● ??

Factors of 42:

1, 2, 3, 6, 7, 14, 21, 42

4 ● 3

5 ● ??

6 ● 7

7 ● 6

Common Factors: 1, 2, 3, 6

Greatest Common Factor: 6

What is the GCF of 18 and 27?

18

27

Factors of 18:

1, 2, 3, 6, 9, 18

1 ● 18

1 ● 27

2 ● ?

2 ● 9

3 ● 9

3 ● 6

Factors of 27:

1, 3, 9, 27

4 ● ?

5 ● ?

4 ● ?

6 ● ?

5 ● ?

7 ● ?

Common Factors: 1, 3, 9

8 ● ?

6 ● 3

9 ● 3

GCF: 9

What is the GCF of 48 and 60?

Factors of 48:

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

48

60

1 ● 48

1 ● 60

2 ● 30

2 ● 24

3 ● 20

3 ● 16

4 ● 15

Factors of 60:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

4 ● 12

5 ● 12

6 ● 8

6 ● 10

Common Factors: 1, 2, 3, 4, 6, 12

GCF: 12

Using Prime Factorization

- Find the prime factorization of each number.
- Identify the common factors and multiply them.

GCF of 27 and 36

27= 3 x 3 x 3

27

36

36= 3 x 3 x 2 x 2

2 x 18

3 x 9

3 x 3 = 9

GCF= 9

2 x 9

3 x 3

3 x 3

Check Your Work- List Factors

12: 1, 2, 3, 4, 6, 12

48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

2. 6: 1, 2, 3, 6

30: 1, 2, 3, 5, 6, 10, 15, 30

3. 12: 1, 2, 3, 4, 6, 12

24: 1, 2, 3, 4, 6, 8, 12, 24

63: 1, 3, 7, 9, 21, 63

Check Your Work- Prime Factorization

12: 2 x 2 x 3

2 x 2 x 3 = 12

48: 2 x 2 x 3 x 2 x 2

2. 6: 2 x 3

2 x 3 = 6

30: 2 x 3 x 5

3. 12: 2 x 2 x 3

24: 2 x 2 x 3 x 2

3

63: 3 x 3 x 3 x 7

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