GCF of 12 and 28
2026-02-28 10:32 Diff
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Last updated on August 5, 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, 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.

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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.

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?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 5

If the GCF of 12 and ‘b’ is 4, and the LCM is 84, find ‘b’.

Okay, lets begin

The value of ‘b’ is 28.

Explanation

GCF x LCM = product of the numbers 4 × 84 = 12 × b

336 = 12b

b = 336 ÷ 12 = 28

Well explained 👍

FAQs on the Greatest Common Factor of 12 and 28

1.What is the LCM of 12 and 28?

The LCM of 12 and 28 is 84.

2.Is 12 divisible by 2?

Yes, 12 is divisible by 2 because it is an even number.

3.What will be the GCF of any two prime numbers?

The common factor of prime numbers is 1 and the number itself. Since 1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.

4.What is the prime factorization of 28?

The prime factorization of 28 is 2² x 7.

5.Are 12 and 28 prime numbers?

No, 12 and 28 are not prime numbers because both of them have more than two factors.

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.