What is the GCF of 51 and 17?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 51 and 17. To solve it, we need to find the largest integer that divides both numbers without leaving a remainder.
Answer
The GCF of 51 and 17 is $17$.
Answer for screen readers
The greatest common factor (GCF) of 51 and 17 is $17$.
Steps to Solve
- List the factors of each number
First, we will identify the factors of both numbers.
- Factors of 51: 1, 3, 17, 51
- Factors of 17: 1, 17
- Identify the common factors
Next, we look for the factors that are common to both lists.
- Common factors of 51 and 17: 1, 17
- Determine the greatest common factor
Now, we choose the largest factor from the common factors we identified.
- The greatest common factor (GCF) is 17.
The greatest common factor (GCF) of 51 and 17 is $17$.
More Information
The greatest common factor is useful in simplifying fractions and finding common denominators. Since 17 is a prime number, it only divides evenly into itself and 1.
Tips
Common mistakes might include:
- Forgetting to list all factors or omitting a factor. To avoid this, ensure you thoroughly check each number.
- Choosing a factor that is not the largest. Always compare the identified common factors and choose the greatest one.
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