105 LearnersLast updated on August 5th, 2025
GCF of 39 and 52
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 39 and 52.
What is the GCF of 39 and 52?
The greatest common factor of 39 and 52 is 13. The largest divisor of two or more numbers is called the GCF of the number. 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 39 and 52?
To find the GCF of 39 and 52, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 39 and 52 by Using Listing of factors
Steps to find the GCF of 39 and 52 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 39 = 1, 3, 13, 39.
Factors of 52 = 1, 2, 4, 13, 26, 52.
Step 2: Now, identify the common factors of them.
Common factors of 39 and 52: 1, 13.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 13.
The GCF of 39 and 52 is 13.
GCF of 39 and 52 Using Prime Factorization
To find the GCF of 39 and 52 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number.
Prime Factors of 39: 39 = 3 x 13
Prime Factors of 52: 52 = 2 x 2 x 13 = 2² x 13
Step 2: Now, identify the common prime factors.
The common prime factor is: 13
Step 3: Multiply the common prime factors 13.
The Greatest Common Factor of 39 and 52 is 13.
GCF of 39 and 52 Using Division Method or Euclidean Algorithm Method
Find the GCF of 39 and 52 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 52 by 39 52 ÷ 39 = 1 (quotient), The remainder is calculated as 52 − (39×1) = 13
The remainder is 13, not zero, so continue the process
Step 2: Now divide the previous divisor (39) by the previous remainder (13)
Divide 39 by 13 39 ÷ 13 = 3 (quotient), remainder = 39 − (13×3) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 39 and 52 is 13.
Common Mistakes and How to Avoid Them in GCF of 39 and 52
Finding the GCF of 39 and 52 looks 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 39, students may mention 6, 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 indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse factors and multiples. In that confusion, sometimes they may write multiples instead of factors. To avoid this confusion, students should clearly know the definitions of multiples and factors.
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 39 and 52 Examples
Problem 1
A gardener has 39 tulips and 52 roses. She wants to arrange them in bouquets with the largest number of flowers in each bouquet. How many flowers will be in each bouquet?
We should find the GCF of 39 and 52 GCF of 39 and 52 is 13.
There are 13 equal bouquets
39 ÷ 13 = 3
52 ÷ 13 = 4
There will be 13 bouquets, and each bouquet gets 3 tulips and 4 roses.
Explanation
As the GCF of 39 and 52 is 13, the gardener can make 13 bouquets.
Now divide 39 and 52 by 13.
Each bouquet gets 3 tulips and 4 roses.
Problem 2
A painter has 39 blue cans and 52 red cans. They want to store them in boxes with the same number of cans in each box, using the largest possible number of cans per box. How many cans will be in each box?
GCF of 39 and 52 is 13. So each box will have 13 cans.
Explanation
There are 39 blue and 52 red cans.
To find the total number of cans in each box, we should find the GCF of 39 and 52.
There will be 13 cans in each box.
Problem 3
A ribbon maker has 39 meters of green ribbon and 52 meters of yellow ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 39 and 52
The GCF of 39 and 52 is 13.
The ribbon is 13 meters long.
Explanation
For calculating the longest length of the ribbon, we first need to calculate the GCF of 39 and 52, which is 13.
The length of each piece of the ribbon will be 13 meters.
Problem 4
A carpenter has two wooden planks, one 39 cm long and the other 52 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The carpenter needs the longest piece of wood
GCF of 39 and 52 is 13.
The longest length of each piece is 13 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 39 cm and 52 cm, respectively. We have to find the GCF of 39 and 52, which is 13 cm.
The longest length of each piece is 13 cm.
Problem 5
If the GCF of 39 and ‘b’ is 13, and the LCM is 156. Find ‘b’.
The value of ‘b’ is 52.
Explanation
GCF x LCM = product of the numbers
13 × 156 = 39 × b
2028 = 39b
b = 2028 ÷ 39 = 52
FAQs on the Greatest Common Factor of 39 and 52
1.What is the LCM of 39 and 52?
2.Is 39 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 52?
5.Are 39 and 52 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 39 and 52?
7.What are some fun ways kids in United States can practice GCF of 39 and 52 with numbers?
8.What role do numbers and GCF of 39 and 52 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 39 and 52 skills?
Important Glossaries for GCF of 39 and 52
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 13 are 1 and 13.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 13 are 13, 26, 39, 52, and so on.
- 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 52 is divided by 39, the remainder is 13.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 39 and 52 is 156.
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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.
