# Finding the Greatest Common Factor

The greatest common factor of two or more whole numbers is the **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.

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

**Example:**

The factors of 36 are

**1, 2, 3**, 4, **6, 9**, 12, **18**, and 36.

The factors of 54 are

**1, 2, 3, 6, 9, 18**, 27, and 54.

The **common factors** of 36 and 54 are

**1, 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**.

**second method**to find the greatest common factor is to list the

**prime factors**, then multiply the common prime factors.

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

**Example:**

**The prime factorization of 36 is**

**2 x 2 x 3 x 3**

**The prime factorization of 54 is**

**2 x 3 x 3 x 3**

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!**

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Further examples of greatest common factor.