What is the greatest common factor of 48 and 84?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 48 and 84. To find this, we will determine the factors of each number and identify the highest factor that both numbers share.
Answer
The greatest common factor (GCF) of 48 and 84 is $12$.
Answer for screen readers
The greatest common factor (GCF) of 48 and 84 is $12$.
Steps to Solve
- List the factors of each number
To find the GCF, first, we need to list the factors of both numbers.
For 48:
- The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
For 84:
- The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
- Identify the common factors
Next, identify which factors are common to both lists.
Common factors of 48 and 84:
- They share the factors: 1, 2, 3, 4, 6, 12
- Determine the greatest common factor
Now, we need to find the greatest value among the common factors identified in the previous step.
The greatest common factor is 12.
The greatest common factor (GCF) of 48 and 84 is $12$.
More Information
The GCF helps simplify fractions and can determine the greatest measure that can be evenly divided into two or more numbers. It's useful in many areas of math, particularly in simplifying ratios or fractions.
Tips
- Ignoring common factors: Sometimes, students may overlook some common factors. It's important to list all factors carefully to identify them all.
- Not verifying factors: Always double-check that identified common factors are indeed factors of both numbers.
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