103 LearnersLast updated on August 5th, 2025
GCF of 12 and 26
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 12 and 26.
What is the GCF of 12 and 26?
The greatest common factor of 12 and 26 is 2. 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 12 and 26?
To find the GCF of 12 and 26, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 12 and 26 by Using Listing of factors
Steps to find the GCF of 12 and 26 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 12 = 1, 2, 3, 4, 6, 12.
Factors of 26 = 1, 2, 13, 26.
Step 2: Now, identify the common factors of them Common factors of 12 and 26: 1, 2.
Step 3: Choose the largest factor
The largest factor that both numbers have is 2.
The GCF of 12 and 26 is 2.
GCF of 12 and 26 Using Prime Factorization
To find the GCF of 12 and 26 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 12: 12 = 2 × 2 × 3 = 2² × 3
Prime Factors of 26: 26 = 2 × 13
Step 2: Now, identify the common prime factors
The common prime factor is: 2
Step 3: Multiply the common prime factors 2
The Greatest Common Factor of 12 and 26 is 2.
GCF of 12 and 26 Using Division Method or Euclidean Algorithm Method
Find the GCF of 12 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 12 26 ÷ 12 = 2 (quotient),
The remainder is calculated as 26 - (12×2) = 2
The remainder is 2, not zero, so continue the process
Step 2: Now divide the previous divisor (12) by the previous remainder (2)
Divide 12 by 2 12 ÷ 2 = 6 (quotient), remainder = 12 - (2×6) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 12 and 26 is 2.
Common Mistakes and How to Avoid Them in GCF of 12 and 26
Finding GCF of 12 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 12, 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 indicates an 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 12 and 26 Examples
Problem 1
A chef has 12 apples and 26 oranges. She wants to arrange them into the largest possible number of identical baskets. How many apples and oranges will be in each basket?
We should find the GCF of 12 and 26 GCF of 12 and 26 2
There are 2 equal groups 12 ÷ 2 = 6 26 ÷ 2 = 13
There will be 2 baskets, and each basket gets 6 apples and 13 oranges.
Explanation
As the GCF of 12 and 26 is 2, the chef can make 2 baskets. Now divide 12 and 26 by 2. Each basket gets 6 apples and 13 oranges.
Problem 2
A park has 12 swings and 26 slides. They want to organize them in sections with the same number of swings and slides in each section, using the largest possible number of sections. How many swings and slides will be in each section?
GCF of 12 and 26 2
So each section will have 2 swings.
Explanation
There are 12 swings and 26 slides. To find the total number of swings and slides in each section, we should find the GCF of 12 and 26. There will be 2 swings and 13 slides in each section.
Problem 3
A tailor has 12 meters of silk and 26 meters of cotton. 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 12 and 26
The GCF of 12 and 26 2
The pieces are 2 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 12 and 26, which is 2. The length of each piece of fabric will be 2 meters.
Problem 4
A carpenter has two wooden planks, one 12 cm long and the other 26 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 12 and 26 2
The longest length of each piece is 2 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 12 cm and 26 cm, respectively, we have to find the GCF of 12 and 26, which is 2 cm. The longest length of each piece is 2 cm.
Problem 5
If the GCF of 12 and ‘b’ is 2, and the LCM is 156, find ‘b’.
The value of ‘b’ is 26.
Explanation
GCF × LCM = product of the numbers 2 × 156 = 12 × b
312 = 12b
b = 312 ÷ 12 = 26
FAQs on the Greatest Common Factor of 12 and 26
1.What is the LCM of 12 and 26?
2.Is 12 divisible by 3?
3.What will be the GCF of any two even numbers?
4.What is the prime factorization of 26?
5.Are 12 and 26 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 12 and 26?
7.What are some fun ways kids in United States can practice GCF of 12 and 26 with numbers?
8.What role do numbers and GCF of 12 and 26 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 12 and 26 skills?
Important Glossaries for GCF of 12 and 26
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- 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 26 is divided by 12, the remainder is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 12 and 26 is 156.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 12 and 26 is 2, 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.
