What is the greatest common factor of 28 and 36?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 28 and 36. To solve this, we will find the factors of both numbers and identify the largest factor that is common to both.
Answer
The greatest common factor (GCF) of 28 and 36 is $4$.
Answer for screen readers
The greatest common factor (GCF) of 28 and 36 is $4$.
Steps to Solve
- Find the factors of 28
To find the factors of 28, we look for all the numbers that divide 28 evenly. The factors of 28 are: 1, 2, 4, 7, 14, and 28.
- Find the factors of 36
Next, we find the factors of 36. The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
- Identify the common factors
Now we list the common factors of both 28 and 36. The common factors are: 1, 2, and 4.
- Determine the greatest common factor
Finally, we identify the largest number from the common factors. The greatest common factor (GCF) is: 4.
The greatest common factor (GCF) of 28 and 36 is $4$.
More Information
The greatest common factor is useful in simplifying fractions, finding common denominators, and solving problems in number theory.
Tips
- A common mistake is not listing all factors accurately. It's essential to check each number carefully.
- Another mistake is assuming that a factor is the GCF without verifying it against all common factors.
