101 LearnersLast updated on August 12th, 2025
GCF of 26 and 52
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 26 and 52.
What is the GCF of 26 and 52?
The greatest common factor of 26 and 52 is 26. 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 26 and 52?
To find the GCF of 26 and 52, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 26 and 52 by Using Listing of Factors
Steps to find the GCF of 26 and 52 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 26 = 1, 2, 13, 26. Factors of 52 = 1, 2, 4, 13, 26, 52.
Step 2: Now, identify the common factors of them Common factors of 26 and 52: 1, 2, 13, 26.
Step 3: Choose the largest factor The largest factor that both numbers have is 26. The GCF of 26 and 52 is 26.
GCF of 26 and 52 Using Prime Factorization
To find the GCF of 26 and 52 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 26: 26 = 2 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 factors are: 2 x 13
Step 3: Multiply the common prime factors 2 x 13 = 26.
The Greatest Common Factor of 26 and 52 is 26.
GCF of 26 and 52 Using Division Method or Euclidean Algorithm Method
Find the GCF of 26 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 26 52 ÷ 26 = 2 (quotient), The remainder is calculated as 52 − (26×2) = 0
The remainder is zero, so the divisor becomes the GCF. The GCF of 26 and 52 is 26.
Common Mistakes and How to Avoid Them in GCF of 26 and 52
Finding the GCF of 26 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 26, students may mention 10, 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 that 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 26 and 52 Examples
Problem 1
A gardener has 26 rose bushes and 52 tulip bulbs. She wants to plant them in equal rows, using the largest number of plants per row. How many plants will be in each row?
We should find the GCF of 26 and 52 GCF of 26 and 52 2 x 13 = 26.
There are 26 equal groups 26 ÷ 26 = 1 52 ÷ 26 = 2
There will be 26 groups, and each group gets 1 rose bush and 2 tulip bulbs.
Explanation
As the GCF of 26 and 52 is 26, the gardener can make 26 rows. Now divide 26 and 52 by 26. Each row gets 1 rose bush and 2 tulip bulbs.
Problem 2
A baker has 26 loaves of whole wheat bread and 52 loaves of sourdough bread. They want to display them in shelves with the same number of loaves on each shelf, using the largest possible number of loaves per shelf. How many loaves will be on each shelf?
GCF of 26 and 52 2 x 13 = 26. So each shelf will have 26 loaves.
Explanation
There are 26 whole wheat and 52 sourdough loaves. To find the total number of loaves on each shelf, we should find the GCF of 26 and 52. There will be 26 loaves on each shelf.
Problem 3
A ribbon maker has 26 meters of red ribbon and 52 meters of blue 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 26 and 52 The GCF of 26 and 52 2 x 13 = 26. The ribbon is 26 meters long.
Explanation
For calculating the longest length of the ribbon, first, we need to calculate the GCF of 26 and 52, which is 26. The length of each piece of the ribbon will be 26 meters.
Problem 4
A carpenter has two wooden planks, one 26 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 26 and 52 2 x 13 = 26. The longest length of each piece is 26 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 26 cm and 52 cm, respectively, we have to find the GCF of 26 and 52, which is 26 cm. The longest length of each piece is 26 cm.
Problem 5
If the GCF of 26 and ‘b’ is 26, and the LCM is 104, find ‘b’.
The value of ‘b’ is 52.
Explanation
GCF x LCM = product of the numbers 26 × 104 = 26 × b 2704 = 26b b = 2704 ÷ 26 = 52
FAQs on the Greatest Common Factor of 26 and 52
1.What is the LCM of 26 and 52?
2.Is 26 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 52?
5.Are 26 and 52 prime numbers?
6.How can children in Thailand use numbers in everyday life to understand GCF of 26 and 52?
7.What are some fun ways kids in Thailand can practice GCF of 26 and 52 with numbers?
8.What role do numbers and GCF of 26 and 52 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve GCF of 26 and 52 skills?
Important Glossaries for GCF of 26 and 52
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 26 are 1, 2, 13, and 26.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, 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 26 are 2 and 13.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 3, the remainder is 2, and the quotient is 4.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 26 and 52 is 52.
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.
