Greatest common factor
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Greatest Common Factor. Lesson 3-3. Greatest Common Factor (GCF). The greatest common factor is the largest factor that two numbers share. Let’s find the GCF of 12 and 42. First, we need to make a list of factors for each number. 12. 42. 1 x 12. 1 x 42. Factors of 12: 1, 2, 3, 4, 6,12.

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Greatest Common Factor

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Greatest common factor

Greatest Common Factor

Lesson 3-3


Greatest common factor gcf

Greatest Common Factor (GCF)

  • The greatest common factor is the largest factor that two numbers share.

  • Let’s find the GCF of 12 and 42. First, we need to make a list of factors for each number.


Greatest common factor

12

42

1 x 12

1 x 42

Factors of 12:

1, 2, 3, 4, 6,12

2 x 21

2 x 6

3 x 14

3 x 4

4 x ??

4 x 3

Factors of 42:

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

5 x ??

6 x 7

7 x 6

Common Factors: 1, 2, 3, 6

Greatest Common Factor: 6


What is the gcf of 18 and 27

What is the GCF of 18 and 27?

18

27

Factors of 18:

1, 2, 3, 6, 9, 18

1 x 18

1 x 27

2 x ?

2 x 9

3 x 9

3 x 6

Factors of 27:

1, 3, 9, 27

4 x ?

5 x ?

4 x ?

6 x ?

5 x ?

7 x ?

Common Factors: 1, 3, 9

8 x ?

6 x 3

9 x 3

GCF: 9


What is the gcf of 48 and 60

What is the GCF of 48 and 60?

Factors of 48:

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

48

60

1 x 48

1 x 60

2 x 30

2 x 24

3 x 20

3 x 16

4 x 15

Factors of 60:

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

4 x 12

5 x 12

6 x 8

6 x 10

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

GCF: 12


Using prime factorization

Using Prime Factorization

  • Find the prime factorization of each number.

  • Identify the common factors and multiply them.


Example gcf of 27 and 36

Example: GCF of 27 and 36

27

36

  • Both prime factorizations have 3x3 in common.

  • Therefore, the GCF is 9.

2 x 18

3 x 9

2 x 9

3 x 3

3 x 3

Ans. 3x3x3

Ans. 2x2x3x3


Homework time

Homework Time


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