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104 LearnersLast updated on September 24, 2025
GCF of 12 and 22
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 12 and 22.
What is the GCF of 12 and 22?
The greatest common factor of 12 and 22 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 22?
To find the GCF of 12 and 22, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 12 and 22 by Using Listing of Factors
Steps to find the GCF of 12 and 22 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 22 = 1, 2, 11, 22.
Step 2: Now, identify the common factors of them. Common factors of 12 and 22: 1, 2.
Step 3: Choose the largest factor. The largest factor that both numbers have is 2.
The GCF of 12 and 22 is 2.
GCF of 12 and 22 Using Prime Factorization
To find the GCF of 12 and 22 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number.
Prime factors of 12: 12 = 2 x 2 x 3 = 2² x 3
Prime factors of 22: 22 = 2 x 11
Step 2: Now, identify the common prime factors. The common prime factor is 2.
Step 3: Multiply the common prime factors. 2 = 2.
The Greatest Common Factor of 12 and 22 is 2.
GCF of 12 and 22 Using Division Method or Euclidean Algorithm Method
Find the GCF of 12 and 22 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number. Here, divide 22 by 12. 22 ÷ 12 = 1 (quotient), The remainder is calculated as 22 − (12×1) = 10.
The remainder is 10, not zero, so continue the process.
Step 2: Now divide the previous divisor (12) by the previous remainder (10). Divide 12 by 10. 12 ÷ 10 = 1 (quotient), remainder = 12 − (10×1) = 2. Continue the process.
Step 3: Now divide the previous divisor (10) by the previous remainder (2). Divide 10 by 2. 10 ÷ 2 = 5 (quotient), remainder = 10 − (2×5) = 0.
The remainder is zero, the divisor will become the GCF. The GCF of 12 and 22 is 2.
Common Mistakes and How to Avoid Them in GCF of 12 and 22
Finding the GCF of 12 and 22 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 5, 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; 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 22 Examples
Problem 1
A gardener has 12 tulip bulbs and 22 daffodil bulbs. She wants to plant them in rows with an equal number of bulbs in each row, using the largest possible number of bulbs per row. How many bulbs will be in each row?
We should find the GCF of 12 and 22. GCF of 12 and 22 is 2.
There are 2 equal groups. 12 ÷ 2 = 6 22 ÷ 2 = 11
There will be 2 groups, and each group gets 6 tulip bulbs and 11 daffodil bulbs.
Explanation
As the GCF of 12 and 22 is 2, the gardener can make 2 groups.
Now divide 12 and 22 by 2.
Each group gets 6 tulip bulbs and 11 daffodil bulbs.
Problem 2
A chef has 12 carrots and 22 potatoes. They want to arrange them in baskets with the same number of vegetables in each basket, using the largest possible number of vegetables per basket. How many vegetables will be in each basket?
GCF of 12 and 22 is 2.
So each basket will have 2 vegetables.
Explanation
There are 12 carrots and 22 potatoes.
To find the total number of vegetables in each basket, we should find the GCF of 12 and 22.
There will be 2 vegetables in each basket.
Problem 3
A tailor has 12 meters of red fabric and 22 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 12 and 22.
The GCF of 12 and 22 is 2.
The fabric is 2 meters long.
Explanation
To calculate the longest length of the fabric pieces, first we need to calculate the GCF of 12 and 22, 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 22 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 22 is 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 22 cm, respectively,
we have to find the GCF of 12 and 22, which is 2 cm.
The longest length of each piece is 2 cm.
Problem 5
If the GCF of 12 and ‘a’ is 2, and the LCM is 132. Find ‘a’.
The value of ‘a’ is 22.
Explanation
GCF x LCM = product of the numbers
2 × 132 = 12 × a
264 = 12a
a = 264 ÷ 12 = 22
FAQs on the Greatest Common Factor of 12 and 22
1.What is the LCM of 12 and 22?
2.Is 12 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 22?
5.Are 12 and 22 prime numbers?
Important Glossaries for GCF of 12 and 22
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 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 22 are 2 and 11.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 22 is divided by 12, the remainder is 10 and the quotient is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 12 and 22 is 132.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 12 and 22 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.
