Last updated on August 5th, 2025
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.
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.
To find the GCF of 12 and 26, a few methods are described below:
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
If the GCF of 12 and ‘b’ is 2, and the LCM is 156, find ‘b’.
The value of ‘b’ is 26.
GCF × LCM = product of the numbers 2 × 156 = 12 × b
312 = 12b
b = 312 ÷ 12 = 26
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.
: She loves to read number jokes and games.