4.3 Greatest Common Factors (GCF)

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

ReviewA factor is number that is multiplied by

another number to get a product

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,

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

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.

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,

Try on your Own

16 & 28

24 & 56

Guided: using Distributive Property

15 + 25

36 + 72

Try on your own

10 + 90=

45 + 72=

LCM

LCM: Least Common Multiple: The smallest number, other than zero, that is a multiple of two or more given numbers

Guided Practice

5 & 6

9 & 11

Try on Your own

3 & 7

4 & 6