gcf 36 48
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 36 and 48. To find the GCF, we need to determine the largest number that divides both 36 and 48 without leaving a remainder.
Answer
The GCF of 36 and 48 is $12$.
Answer for screen readers
The greatest common factor of 36 and 48 is 12.
Steps to Solve
- Find the factors of 36
List the factors of 36. The factors are the numbers that divide 36 evenly. The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36.
- Find the factors of 48
Next, list the factors of 48 in the same manner. The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
- Identify the common factors
Now, identify the factors that are common to both lists of factors from steps 1 and 2. The common factors are: 1, 2, 3, 4, 6, 12.
- Find the greatest common factor
Finally, determine the largest common factor from the list identified in step 3. The greatest common factor (GCF) is 12.
The greatest common factor of 36 and 48 is 12.
More Information
The GCF is useful in simplifying fractions, finding common denominators, and solving problems involving ratios. It represents the largest number that can evenly divide both numbers, making it a key concept in number theory.
Tips
- Not listing all factors: Sometimes, students miss one or more factors. Make sure to list all numbers that divide evenly.
- Overlooking larger common factors: Focusing only on small numbers can lead to missing the largest GCF. Always check all common factors for the greatest one.
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