What is the greatest common factor of 17 and 51?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 17 and 51. To find the GCF, we need to identify the largest positive integer that divides both numbers without leaving a remainder.
Answer
The GCF of 17 and 51 is \(17\).
Answer for screen readers
The greatest common factor (GCF) of 17 and 51 is (17).
Steps to Solve
- List the Factors of Each Number
First, we will find the factors for both numbers.
Factors of 17: $1, 17$
Factors of 51: $1, 3, 17, 51$
- Identify Common Factors
Next, we need to identify the common factors between the two lists.
Common factors of 17 and 51: $1, 17$
- Find the Greatest Common Factor
Finally, we select the largest number from the common factors identified.
The greatest common factor is (17).
The greatest common factor (GCF) of 17 and 51 is (17).
More Information
The GCF is useful in simplifying fractions and finding common denominators. Notably, 17 is a prime number, meaning its only factors are 1 and itself. Therefore, in this case, the GCF is also 17.
Tips
- A common mistake is forgetting to include 1 as a factor. Always remember that 1 is a factor of every integer.
- Misidentifying the factors, especially in larger numbers. Make sure to check your factor pairs systematically.
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