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104 LearnersLast updated on October 7, 2025
GCF of 13 and 26
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 13 and 26.
What is the GCF of 13 and 26?
The greatest common factor of 13 and 26 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 13 and 26?
To find the GCF of 13 and 26, a few methods are described below -
Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm
GCF of 13 and 26 by Using Listing of factors
Steps to find the GCF of 13 and 26 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 13 = 1, 13 Factors of 26 = 1, 2, 13, 26.
Step 2: Now, identify the common factors of them Common factors of 13 and 26: 1, 13.
Step 3: Choose the largest factor,The largest factor that both numbers have is 13.
The GCF of 13 and 26 is 13.
GCF of 13 and 26 Using Prime Factorization
To find the GCF of 13 and 26 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 13: 13 Prime Factors of 26: 2 × 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 26 is 13.
GCF of 13 and 26 Using Division Method or Euclidean Algorithm Method
Find the GCF of 13 and 26 using the division method or Euclidean Algorithm Method.
Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 26 by 13 26 ÷ 13 = 2 (quotient), The remainder is calculated as 26 − (13×2) = 0 The remainder is zero, so the divisor is the GCF.
The GCF of 13 and 26 is 13.
Common Mistakes and How to Avoid Them in GCF of 13 and 26
Finding the GCF of 13 and 26 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 13, students may mention 2 or 3, which are 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 and 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 26 Examples
Problem 1
A gardener has 13 pots and 26 plants. She wants to distribute the plants into the pots equally, with the largest number of plants in each pot. How many plants will be in each pot?
We should find the GCF of 13 and 26.
The GCF of 13 and 26 is 13.
There will be 13 pots, and each pot will have 2 plants.
Explanation
As the GCF of 13 and 26 is 13, the gardener can distribute 2 plants per pot equally across all 13 pots.
Problem 2
A contractor has 13 meters of cable and 26 meters of wire. He wants to cut them into the longest possible equal lengths without any leftover. What should be the length of each piece?
To find the longest equal length, we have to calculate the GCF of 13 and 26.
The GCF of 13 and 26 is 13.
Each piece will be 13 meters long.
Explanation
To find the longest length of each piece of cable and wire, we calculate the GCF of 13 and 26.
Each piece will be 13 meters long.
Problem 3
A chef has 13 eggs and 26 slices of bread. He wants to make the largest number of identical sandwiches with these ingredients. How many sandwiches can he make?
For calculating the maximum number of sandwiches, we need the GCF of 13 and 26.
The GCF of 13 and 26 is 13.
He can make 13 identical sandwiches.
Explanation
For making the maximum number of identical sandwiches, find the GCF of 13 and 26, which is 13.
The chef can make 13 sandwiches.
Problem 4
A teacher has 13 notebooks and 26 pencils. She wants to distribute them in sets with the largest equal number of notebooks and pencils in each set. How many sets can she make?
The teacher needs to find the largest number of sets.
The GCF of 13 and 26 is 13.
She can make 13 sets.
Explanation
To find the largest number of sets, the teacher needs the GCF of 13 and 26, which is 13.
She can make 13 sets.
Problem 5
If the GCF of 13 and ‘b’ is 13, and the LCM is 26. Find ‘b’.
The value of ‘b’ is 26.
Explanation
GCF × LCM = product of the numbers 13 × 26 = 13 × b 338 = 13b b = 338 ÷ 13 = 26
FAQs on the Greatest Common Factor of 13 and 26
1.What is the LCM of 13 and 26?
2.Is 13 a prime number?
3.What will be the GCF of any number and 1?
4.What is the prime factorization of 26?
5.Are 13 and 26 prime numbers?
Important Glossaries for GCF of 13 and 26
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 26 are 1, 2, 13, and 26.
- Prime Number: A number greater than 1 that has no positive divisors other than 1 and itself. For example, 13 is a prime number.
- Common Factors: Numbers that are factors of two or more numbers. For example, the common factors of 13 and 26 are 1 and 13.
- Euclidean Algorithm: A method to find the GCF of two numbers by repeated division.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 13 and 26 is 13.
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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.
