**largest whole number**that divides evenly into each of the numbers. There are

**two ways**to find the greatest common factor.

The **first method** is to list all of the factors of each number, then list the **common factors** and choose the largest one.

**Example**:

Find the **GCF** of 36 and 54.

The factors of 36 are

1,2,3, 4,6,9, 12,, and 36.18The factors of 54 are

1,2,3,6,9,, 27, and 54.18The

common factorsof 36 and 54 are1, 2, 3, 6, 9, 18

Although the numbers in **bold** are all common factors of both 36 and 54, ** 18** is the

**greatest common factor**.

The **second method** for finding the greatest common factor is to list the **prime factors**, then multiply the common prime factors.

**Example**:

Let's use the same numbers, 36 and 54 again to find their greatest common multiple.

The prime factorization of 36 is

2x 2 x3x3The prime factorization of 54 is

2x 3 x3x3

Notice that the prime factorizations of 36 and 54 both have **one** **2** and **two** **3s** in common. So, we simply **multiply** these common prime factors to find the greatest common factor. **Like this...**

2 x 3 x 3 = 18

**Both methods for finding the greatest common factor work!**