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107 LearnersLast updated on August 12, 2025
GCF of 26 and 65
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 65.
What is the GCF of 26 and 65?
The greatest common factor of 26 and 65 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 26 and 65?
To find the GCF of 26 and 65, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 26 and 65 by Using Listing of Factors
Steps to find the GCF of 26 and 65 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 26 = 1, 2, 13, 26. Factors of 65 = 1, 5, 13, 65.
Step 2: Now, identify the common factors of them Common factors of 26 and 65: 1, 13.
Step 3: Choose the largest factor The largest factor that both numbers have is 13. The GCF of 26 and 65 is 13.
GCF of 26 and 65 Using Prime Factorization
To find the GCF of 26 and 65 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 65: 65 = 5 x 13
Step 2: Now, identify the common prime factors The common prime factor is: 13
Step 3: Multiply the common prime factors 13 = 13. The Greatest Common Factor of 26 and 65 is 13.
GCF of 26 and 65 Using Division Method or Euclidean Algorithm Method
Find the GCF of 26 and 65 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 65 by 26 65 ÷ 26 = 2 (quotient), The remainder is calculated as 65 − (26×2) = 13 The remainder is 13, not zero, so continue the process
Step 2: Now divide the previous divisor (26) by the previous remainder (13) Divide 26 by 13 26 ÷ 13 = 2 (quotient), remainder = 26 − (13×2) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 26 and 65 is 13.
Common Mistakes and How to Avoid Them in GCF of 26 and 65
Finding GCF of 26 and 65 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 between 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 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 65 Examples
Problem 1
A chef has 26 apples and 65 oranges. He wants to arrange them into the largest possible equal groups. How many fruits will be in each group?
We should find the GCF of 26 and 65 GCF of 26 and 65 is 13. There are 13 equal groups 26 ÷ 13 = 2 65 ÷ 13 = 5
There will be 13 groups, and each group gets 2 apples and 5 oranges.
Explanation
As the GCF of 26 and 65 is 13, the chef can make 13 groups. Now divide 26 and 65 by 13. Each group gets 2 apples and 5 oranges.
Problem 2
A school has 26 red flags and 65 blue flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?
GCF of 26 and 65 is 13. So each row will have 13 flags.
Explanation
There are 26 red and 65 blue flags. To find the total number of flags in each row, we should find the GCF of 26 and 65. There will be 13 flags in each row.
Problem 3
A tailor has 26 meters of red fabric and 65 meters of blue fabric. She wants to cut both fabrics 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 65 The GCF of 26 and 65 is 13. The fabric is 13 meters long.
Explanation
For calculating the longest length of the fabric first we need to calculate the GCF of 26 and 65 which is 13.
The length of each piece of the fabric will be 13 meters.
Problem 4
A carpenter has two wooden planks, one 26 cm long and the other 65 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 65 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, 26 cm and 65 cm, respectively, we have to find the GCF of 26 and 65, which is 13 cm. The longest length of each piece is 13 cm.
Problem 5
If the GCF of 26 and ‘b’ is 13, and the LCM is 130. Find ‘b’.
The value of ‘b’ is 65.
Explanation
GCF x LCM = product of the numbers
13 × 130 = 26 × b
1690 = 26b
b = 1690 ÷ 26 = 65
FAQs on the Greatest Common Factor of 26 and 65
1.What is the LCM of 26 and 65?
2.Is 26 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 65?
5.Are 26 and 65 prime numbers?
Important Glossaries for GCF of 26 and 65
- 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 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 15 is divided by 4, the remainder is 3.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 26 and 65 is 13, as it is their largest common factor that divides the numbers completely.
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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.
