What is the greatest common factor of 75 and 125?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 75 and 125. To find this, we will determine the factors of each number and identify the largest factor that they share.
Answer
The greatest common factor is $25$.
Answer for screen readers
The greatest common factor (GCF) of $75$ and $125$ is $25$.
Steps to Solve
- List the factors of each number
First, we need to identify the factors of both numbers.
- The factors of $75$ are $1, 3, 5, 15, 25, 75$.
- The factors of $125$ are $1, 5, 25, 125$.
- Identify the common factors
Next, we will find the factors that are common between the two lists:
- The common factors of $75$ and $125$ are $1, 5, 25$.
- Determine the greatest common factor
To find the greatest common factor, we compare the common factors and identify the largest one:
- The largest common factor is $25$.
The greatest common factor (GCF) of $75$ and $125$ is $25$.
More Information
The GCF is useful in simplifying fractions, finding equivalent ratios, and solving problems involving least common multiples. It's a fundamental concept in number theory and helps in various applications in math.
Tips
- Forgetting to list all factors may lead to missing the GCF. Make sure to write down all factors carefully.
- Overlooking the largest common factor by misidentifying it among shared factors. Always double-check comparisons.
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