What is the GCF of 54 and 42?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 54 and 42. To solve this, we will find the factors of both numbers and determine the largest factor they have in common.
Answer
$6$
Answer for screen readers
The greatest common factor (GCF) of 54 and 42 is $6$.
Steps to Solve
- List the Factors of Each Number
First, we'll find the factors of 54. The factors of 54 are the numbers that can divide 54 without leaving a remainder:
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54.
Next, we find the factors of 42:
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42.
- Identify the Common Factors
Now that we have the factors for both numbers, we identify the common factors between them:
Common factors of 54 and 42: 1, 2, 3, 6.
- Determine the Greatest Common Factor (GCF)
The final step is to find the largest number in the list of common factors, which is the GCF:
The GCF of 54 and 42 is 6.
The greatest common factor (GCF) of 54 and 42 is $6$.
More Information
The GCF is helpful in simplifying fractions, finding common denominators, and solving problems in number theory. Finding the GCF can also aid in numerous real-world applications, such as distributing items evenly.
Tips
- Forgetting to list all the factors can lead to a missed common factor. Always make sure to check all possibilities up to the number itself.
- Confusing the GCF with the least common multiple (LCM). Remember, GCF finds the greatest factor common to both numbers, whereas LCM finds the smallest multiple common to both.
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