100 LearnersLast updated on August 5th, 2025
GCF of 12 and 28
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 12 and 28.
What is the GCF of 12 and 28?
The greatest common factor of 12 and 28 is 4. The largest divisor of two or more numbers is called the GCF of the numbers. 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 28?
To find the GCF of 12 and 28, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 12 and 28 by Using Listing of Factors
Steps to find the GCF of 12 and 28 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 28 = 1, 2, 4, 7, 14, 28.
Step 2: Now, identify the common factors of them Common factors of 12 and 28: 1, 2, 4.
Step 3: Choose the largest factor
The largest factor that both numbers have is 4.
The GCF of 12 and 28 is 4.
GCF of 12 and 28 Using Prime Factorization
To find the GCF of 12 and 28 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 28: 28 = 2 x 2 x 7 = 2² x 7
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 2 = 2²
Step 3: Multiply the common prime factors 2² = 4.
The Greatest Common Factor of 12 and 28 is 4.
GCF of 12 and 28 Using Division Method or Euclidean Algorithm Method
Find the GCF of 12 and 28 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 28 by 12
28 ÷ 12 = 2 (quotient), remainder is calculated as 28 − (12×2) = 4
The remainder is 4, not zero, so continue the process
Step 2: Now divide the previous divisor (12) by the previous remainder (4)
Divide 12 by 4 12 ÷ 4 = 3 (quotient), remainder = 12 − (4×3) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 12 and 28 is 4.
Common Mistakes and How to Avoid Them in GCF of 12 and 28
Finding GCF of 12 and 28 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 factors with 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 28 Examples
Problem 1
A gardener has 12 rose plants and 28 tulip plants. She wants to arrange them in equal rows with the largest number of plants in each row. How many plants will be in each row?
We should find the GCF of 12 and 28 GCF of 12 and 28 2² = 4.
There are 4 equal groups 12 ÷ 4 = 3 28 ÷ 4 = 7
There will be 4 groups, and each group gets 3 rose plants and 7 tulip plants.
Explanation
As the GCF of 12 and 28 is 4, the gardener can make 4 groups. Now divide 12 and 28 by 4. Each group gets 3 rose plants and 7 tulip plants.
Problem 2
A coach has 12 footballs and 28 basketballs. He wants to store them in bins with the same number of balls in each bin, using the largest possible number of balls per bin. How many balls will be in each bin?
GCF of 12 and 28 2² = 4. So each bin will have 4 balls.
Explanation
There are 12 footballs and 28 basketballs. To find the total number of balls in each bin, we should find the GCF of 12 and 28. There will be 4 balls in each bin.
Problem 3
A chef has 12 kg of flour and 28 kg of sugar. She wants to pack them into bags of equal weight, using the largest possible weight for each bag. What should be the weight of each bag?
For calculating the largest equal weight, we have to calculate the GCF of 12 and 28
The GCF of 12 and 28 2² = 4.
Each bag will weigh 4 kg.
Explanation
For calculating the largest weight of the bags first, we need to calculate the GCF of 12 and 28, which is 4. The weight of each bag will be 4 kg.
Problem 4
A builder has two beams, one 12 meters long and the other 28 meters 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 builder needs the longest piece of wood GCF of 12 and 28 2² = 4.
The longest length of each piece is 4 meters.
Explanation
To find the longest length of each piece of the two beams, 12 meters and 28 meters, respectively, we have to find the GCF of 12 and 28, which is 4 meters. The longest length of each piece is 4 meters.
Problem 5
If the GCF of 12 and ‘b’ is 4, and the LCM is 84, find ‘b’.
The value of ‘b’ is 28.
Explanation
GCF x LCM = product of the numbers 4 × 84 = 12 × b
336 = 12b
b = 336 ÷ 12 = 28
FAQs on the Greatest Common Factor of 12 and 28
1.What is the LCM of 12 and 28?
2.Is 12 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 28?
5.Are 12 and 28 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 12 and 28?
7.What are some fun ways kids in United States can practice GCF of 12 and 28 with numbers?
8.What role do numbers and GCF of 12 and 28 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 28 skills?
Important Glossaries for GCF of 12 and 28
- 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 28 are 2 and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 28 is divided by 12, the remainder is 4.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 12 and 28 is 84.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 12 and 28 is 4, 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.
