What is the GCF of 13 and 39?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 13 and 39. To determine the GCF, one would look for the largest number that divides both integers without leaving a remainder.
Answer
$13$
Answer for screen readers
The greatest common factor (GCF) of 13 and 39 is $13$.
Steps to Solve
- Identify the factors of each number
List the factors of 13 and 39.
Factors of 13:
- 1, 13 (since 13 is a prime number, its only factors are itself and 1)
Factors of 39:
- 1, 3, 13, 39 (to find these, divide 39 by numbers starting from 1 up to 39)
- Find the common factors
Now identify the factors that both numbers share.
Common factors of 13 and 39 are:
- 1, 13
- Determine the greatest common factor
Among the common factors, select the greatest one.
The GCF of 13 and 39 is:
- 13
The greatest common factor (GCF) of 13 and 39 is $13$.
More Information
The GCF is useful in simplifying fractions, finding common denominators, and solving problems involving divisibility. In this case, since 13 is prime and divides 39 evenly, it becomes an example of a number's relationship with its multiples.
Tips
- A common mistake might be confusing the GCF with the least common multiple (LCM). It's important to remember that GCF is about finding the largest factor, while LCM deals with the smallest multiple.
