What is the greatest common factor of 75 and 100?
Understand the Problem
The question is asking us to find the greatest common factor (GCF) of the numbers 75 and 100, which involves determining the largest number that divides both of these numbers evenly.
Answer
$25$
Answer for screen readers
The GCF of 75 and 100 is $25$.
Steps to Solve
- List the factors of each number
First, we will find the factors of 75 and 100.
Factors of 75: $1, 3, 5, 15, 25, 75$
Factors of 100: $1, 2, 4, 5, 10, 20, 25, 50, 100$
- Identify the common factors
Next, we determine which factors are common to both lists.
Common factors of 75 and 100: $1, 5, 25$
- Determine the greatest common factor
Now, we find the largest factor that is common to both numbers.
The greatest common factor (GCF) is $25$.
The GCF of 75 and 100 is $25$.
More Information
The greatest common factor (GCF) is useful in simplifying fractions or determining the smallest shared multiple between numbers. Knowing how to find the GCF can help in various mathematical applications, such as simplifying ratios and fractions.
Tips
- Forgetting to list all factors: Ensure that you check each number thoroughly to avoid missing factors.
- Confusing factors with multiples: Factors divide evenly into a number while multiples are produced by multiplying the number.
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