103 LearnersLast updated on August 5th, 2025
GCF of 13 and 39
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 13 and 39.
What is the GCF of 13 and 39?
The greatest common factor of 13 and 39 is 13. The largest divisor of two or more numbers is called the GCF of the numbers. If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1. The GCF of two numbers cannot be negative because divisors are always positive.
How to find the GCF of 13 and 39?
To find the GCF of 13 and 39, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / Euclidean Algorithm
GCF of 13 and 39 by Using Listing of Factors
Steps to find the GCF of 13 and 39 using the listing of factors:
Step 1: Firstly, list the factors of each number.
Factors of 13 = 1, 13.
Factors of 39 = 1, 3, 13, 39.
Step 2: Now, identify the common factors of them.
Common factors of 13 and 39: 1, 13.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 13.
The GCF of 13 and 39 is 13.
GCF of 13 and 39 Using Prime Factorization
To find the GCF of 13 and 39 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number.
Prime Factors of 13: 13 is a prime number, so it has only itself as a prime factor.
Prime Factors of 39: 39 = 3 x 13.
Step 2: Now, identify the common prime factors.
The common prime factor is 13.
Step 3: Multiply the common prime factors.
The Greatest Common Factor of 13 and 39 is 13.
GCF of 13 and 39 Using Division Method or Euclidean Algorithm Method
Find the GCF of 13 and 39 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number.
Here, divide 39 by 13. 39 ÷ 13 = 3 (quotient), The remainder is calculated as 39 − (13×3) = 0.
The remainder is zero, so the divisor will become the GCF.
The GCF of 13 and 39 is 13.
Common Mistakes and How to Avoid Them in GCF of 13 and 39
Finding the GCF of 13 and 39 seems simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 13, students may mention 2, which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the Wrong Common Factor
Students may sometimes select the smallest common factor instead of the largest one. To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to Include 1 as a Factor
Sometimes students may forget 1 as a common factor of the numbers. However, it does not affect the GCF, but it tells about the incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors with multiples. In that confusion, sometimes they may write multiples instead of factors. To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is Always an Even Number
Students may assume that the GCF of two numbers will always be an even number. But it's not true; a GCF can also be an odd number. To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 13 and 39 Examples
Problem 1
A librarian has 13 fiction books and 39 non-fiction books. She wants to arrange them in equal stacks, with each stack having the largest number of books possible. How many books will be in each stack?
We should find the GCF of 13 and 39. GCF of 13 and 39 is 13.
There are 13 equal stacks.
13 ÷ 13 = 1
39 ÷ 13 = 3
There will be 13 stacks, and each stack gets 1 fiction book and 3 non-fiction books.
Explanation
As the GCF of 13 and 39 is 13, the librarian can make 13 stacks.
Now divide 13 and 39 by 13.
Each stack gets 1 fiction book and 3 non-fiction books.
Problem 2
A farmer has 13 apple trees and 39 orange trees. He wants to plant them in rows with the same number of trees in each row, using the largest possible number of trees per row. How many trees will be in each row?
GCF of 13 and 39 is 13. So each row will have 13 trees.
Explanation
There are 13 apple trees and 39 orange trees.
To find the total number of trees in each row, we should find the GCF of 13 and 39.
There will be 13 trees in each row.
Problem 3
A chef has 13 kilograms of flour and 39 kilograms of sugar. She wants to package them in bags of equal weight, using the largest possible weight for each bag. What should be the weight of each bag?
For calculating the largest equal weight, we have to calculate the GCF of 13 and 39.
The GCF of 13 and 39 is 13.
Each bag will weigh 13 kilograms.
Explanation
For calculating the largest weight for each bag, we first need to calculate the GCF of 13 and 39, which is 13. The weight of each bag will be 13 kilograms.
Problem 4
A decorator has two ribbons, one 13 meters long and the other 39 meters long. She wants to cut them into the longest possible equal pieces, without any ribbon left over. What should be the length of each piece?
The decorator needs the longest piece of ribbon.
GCF of 13 and 39 is 13.
The longest length of each piece is 13 meters.
Explanation
To find the longest length of each piece of the two ribbons, 13 meters and 39 meters, respectively, we have to find the GCF of 13 and 39, which is 13 meters. The longest length of each piece is 13 meters.
Problem 5
If the GCF of 13 and ‘b’ is 13, and the LCM is 39, find ‘b’.
The value of ‘b’ is 39.
Explanation
GCF x LCM = product of the numbers
13 × 39 = 13 × b
507 = 13b
b = 507 ÷ 13 = 39
FAQs on the Greatest Common Factor of 13 and 39
1.What is the LCM of 13 and 39?
2.Is 13 a prime number?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 39?
5.Are 13 and 39 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 13 and 39?
7.What are some fun ways kids in United States can practice GCF of 13 and 39 with numbers?
8.What role do numbers and GCF of 13 and 39 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve GCF of 13 and 39 skills?
Important Glossaries for GCF of 13 and 39
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 13 are 1 and 13.
- Prime Numbers: Numbers that have only two distinct positive divisors: 1 and the number itself. For example, 13 is a prime number.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 39 are 3 and 13.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 39 is divided by 13, the remainder is 0.
- LCM: The smallest common multiple of two or more numbers is termed the LCM. For example, the LCM of 13 and 39 is 39.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
