What is the GCF of 21 and 28?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 21 and 28, which involves finding the largest integer that divides both numbers without leaving a remainder.
Answer
The greatest common factor (GCF) of 21 and 28 is $7$.
Answer for screen readers
The greatest common factor (GCF) of 21 and 28 is 7.
Steps to Solve
- List the factors of each number
We begin by finding all the factors of 21 and 28.
- Factors of 21 are: 1, 3, 7, 21
- Factors of 28 are: 1, 2, 4, 7, 14, 28
- Identify the common factors
Next, we look for the factors that both numbers share. From the factors listed:
- Common factors of 21 and 28 are: 1, 7
- Determine the greatest common factor
Now, we find the largest number from the common factors. The largest common factor is 7.
The greatest common factor (GCF) of 21 and 28 is 7.
More Information
The greatest common factor is useful in many applications, including simplifying fractions and finding common denominators.
Tips
- A common mistake is to select a factor that is not common to both numbers; always double-check the factors.
- Another mistake is to overlook larger common factors if they exist; ensure that you identify all common factors before selecting the greatest one.
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