# What is the GCF of 10 and 30?

#### Understand the Problem

The question is asking for the greatest common factor (GCF) of the numbers 10 and 30. To solve this, we need to determine the largest number that divides both 10 and 30 without leaving a remainder.

#### Answer

The greatest common factor (GCF) of 10 and 30 is $10$.
##### Answer for screen readers

The greatest common factor (GCF) of 10 and 30 is $10$.

#### Steps to Solve

1. List the factors of each number

First, we find all the factors of 10 and 30.

• Factors of 10: 1, 2, 5, 10
• Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
1. Identify the common factors

Next, we identify the factors that both numbers share.

• Common factors of 10 and 30: 1, 2, 5, 10
1. Determine the greatest common factor

Now, we find the largest factor from the common factors identified.

The greatest common factor is 10.

The greatest common factor (GCF) of 10 and 30 is $10$.

#### More Information

The GCF is useful in various applications such as simplifying fractions or finding common denominators. It shows the largest number that can divide into the numbers without leaving a remainder.

#### Tips

• Forgetting to list all factors of both numbers can lead to missing common factors. Make sure to double-check that all factors are accounted for.
• Misidentifying the greatest common factor by mistakenly choosing a smaller common factor. Always double-check to find the largest one.
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