What is the GCF of 26 and 34?
Understand the Problem
The question is asking for the greatest common factor (GCF) between the numbers 26 and 34, which means we need to find the largest number that divides both 26 and 34 without leaving a remainder.
Answer
The greatest common factor (GCF) of 26 and 34 is \(2\).
Answer for screen readers
The greatest common factor (GCF) of 26 and 34 is (2).
Steps to Solve
- List the factors of each number First, we will identify the factors of both 26 and 34.
- The factors of 26 are: 1, 2, 13, and 26.
- The factors of 34 are: 1, 2, 17, and 34.
- Identify the common factors Next, we list the common factors of both sets.
- Common factors of 26 and 34 are: 1 and 2.
- Find the greatest common factor Now we will determine the greatest of the common factors identified.
- The greatest common factor is 2.
The greatest common factor (GCF) of 26 and 34 is (2).
More Information
The GCF is useful in simplifying fractions, finding common denominators, and solving problems involving divisibility. The GCF approach shows how numbers can share divisors, which is foundational in number theory.
Tips
One common mistake is forgetting to list all factors or incorrectly identifying common factors. To avoid this, ensure you write out all factors carefully for each number.
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