What is the greatest common factor of 42 and 48?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 42 and 48, which is the largest number that divides both 42 and 48 without leaving a remainder. To find this, we can list the factors of both numbers and identify the highest one they share.
Answer
The greatest common factor (GCF) of 42 and 48 is $6$.
Answer for screen readers
The greatest common factor (GCF) of 42 and 48 is $6$.
Steps to Solve
- List the factors of each number
We start by finding the factors of 42. The factors are: 1, 2, 3, 6, 7, 14, 21, 42.
Next, we find the factors of 48. The factors are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
- Identify the common factors
Now, we compare the factors of both numbers to find the common factors. The common factors of 42 and 48 are: 1, 2, 3, 6.
- Find the greatest common factor (GCF)
The greatest common factor is the highest number among the common factors. From the list of common factors (1, 2, 3, 6), the highest number is 6.
Thus, $GCF(42, 48) = 6$.
The greatest common factor (GCF) of 42 and 48 is $6$.
More Information
The GCF is useful in various mathematical applications, such as simplifying fractions, finding common denominators, and solving problems related to ratios. Understanding how to find the GCF can greatly enhance overall problem-solving skills in mathematics.
Tips
One common mistake is overlooking a factor or miscounting the factors. To avoid this, it's helpful to double-check the list of factors for each number to ensure all are correctly included.
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