What is the greatest common factor of 26 and 34?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 26 and 34. To find the GCF, we can identify the prime factors of each number and determine the largest factor they share.
Answer
$2$
Answer for screen readers
The GCF of 26 and 34 is $2$.
Steps to Solve
- Find the prime factors of 26
To find the prime factors, divide 26 by the smallest prime numbers.
Starting with 2: $$ 26 \div 2 = 13 $$
So, the prime factors of 26 are 2 and 13.
- Find the prime factors of 34
Now, let's find the prime factors of 34 using the same method.
Starting with 2: $$ 34 \div 2 = 17 $$
Thus, the prime factors of 34 are 2 and 17.
- Identify the common factors
Now that we have the prime factors:
- Prime factors of 26: 2, 13
- Prime factors of 34: 2, 17
The common factor in both lists is 2.
- Determine the GCF
The greatest common factor (GCF) is the largest of the common factors identified.
Since the only common factor is 2, the GCF of 26 and 34 is 2.
The GCF of 26 and 34 is $2$.
More Information
The greatest common factor (GCF) is useful in various applications, such as simplifying fractions or solving problems involving ratios. Understanding GCF can help in factoring and finding common denominators as well.
Tips
- Not finding all prime factors: Always ensure to check all small prime numbers when identifying prime factors.
- Ignoring prime factorization: It can be easy to overlook simpler common divisors; ensure to thoroughly list factors before concluding.
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