# What is the GCF of 20 and 45?

#### Understand the Problem

The question is asking for the greatest common factor (GCF) of the numbers 20 and 45. The GCF is the largest positive integer that divides both numbers without leaving a remainder. To solve this, we will factor each number and identify the common factors.

The GCF of 20 and 45 is $5$.

The greatest common factor (GCF) of 20 and 45 is 5.

#### Steps to Solve

1. List the factors of each number

First, we need to find all the factors of 20 and 45.

• Factors of 20: 1, 2, 4, 5, 10, 20
• Factors of 45: 1, 3, 5, 9, 15, 45
1. Identify the common factors

Next, we will identify the factors that both numbers share.

• The common factors of 20 and 45 are: 1 and 5.
1. Determine the greatest common factor

Finally, we will select the largest number from the common factors identified.

• The greatest common factor (GCF) is 5.

The greatest common factor (GCF) of 20 and 45 is 5.

The greatest common factor is useful for simplifying fractions or finding least common multiples. The GCF can also be a key step in number theory problems.

#### Tips

Common mistakes include:

• Forgetting to list all factors for at least one of the numbers, which can lead to an incomplete set of common factors.
• Mistaking the smallest common factor for the greatest common factor.
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