# What is the greatest common factor of 32 and 54?

#### Understand the Problem

The question is asking us to find the greatest common factor (GCF) of the numbers 32 and 54. To solve it, we will determine the factors of each number and identify the largest factor that is common to both.

The greatest common factor (GCF) of 32 and 54 is $2$.

The greatest common factor (GCF) of 32 and 54 is $2$.

#### Steps to Solve

1. Find the factors of 32

To find the factors, we need to determine all the numbers that divide 32 evenly. The factors of 32 are: 1, 2, 4, 8, 16, 32

1. Find the factors of 54

Next, we do the same for 54. The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54

1. Identify common factors

Now, we look for the factors that appear in both lists. The common factors of 32 and 54 are: 1, 2

1. Determine the greatest common factor

From the common factors, we identify the greatest one. The greatest common factor (GCF) of 32 and 54 is: 2

The greatest common factor (GCF) of 32 and 54 is $2$.

The greatest common factor is a way to find the largest resuable component of two numbers. It's useful in simplifying fractions, finding equivalent ratios, and even in real-life situations like dividing goods into the largest possible groups.

#### Tips

Common mistakes include:

• Listing factors incorrectly. Make sure to divide the number correctly to find all factors.
• Forgetting to check each number for commonality. Always check both sets of factors thoroughly.
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