GCF of 28 and 20
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Last updated on September 19, 2025

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 28 and 20.

What is the GCF of 28 and 20?

The greatest common factor of 28 and 20 is 4. 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 28 and 20?

To find the GCF of 28 and 20, a few methods are described below 

  • Listing Factors
     
  • Prime Factorization
     
  • Long Division Method / by Euclidean Algorithm

GCF of 28 and 20 by Using Listing of Factors

Steps to find the GCF of 28 and 20 using the listing of factors

Step 1: Firstly, list the factors of each number

Factors of 28 = 1, 2, 4, 7, 14, 28.

Factors of 20 = 1, 2, 4, 5, 10, 20.

Step 2: Now, identify the common factors of them Common factors of 28 and 20: 1, 2, 4.

Step 3: Choose the largest factor The largest factor that both numbers have is 4.

The GCF of 28 and 20 is 4.

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GCF of 28 and 20 Using Prime Factorization

To find the GCF of 28 and 20 using Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number

Prime Factors of 28: 28 = 2 x 2 x 7 = 2² x 7

Prime Factors of 20: 20 = 2 x 2 x 5 = 2² x 5

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 28 and 20 is 4.

GCF of 28 and 20 Using Division Method or Euclidean Algorithm Method

Find the GCF of 28 and 20 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 20 28 ÷ 20 = 1 (quotient),

The remainder is calculated as 28 − (20×1) = 8

The remainder is 8, not zero, so continue the process

Step 2: Now divide the previous divisor (20) by the previous remainder (8)

Divide 20 by 8 20 ÷ 8 = 2 (quotient), remainder = 20 − (8×2) = 4

Step 3: Now divide the previous divisor (8) by the previous remainder (4)

Divide 8 by 4 8 ÷ 4 = 2 (quotient), remainder = 8 − (4×2) = 0

The remainder is zero, the divisor will become the GCF.

The GCF of 28 and 20 is 4.

Common Mistakes and How to Avoid Them in GCF of 28 and 20

Finding GCF of 28 and 20 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 teacher has 28 apples and 20 oranges. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?

Okay, lets begin

We should find GCF of 28 and 20 GCF of 28 and 20 2² = 4.

There are 4 equal groups 28 ÷ 4 = 7 20 ÷ 4 = 5

There will be 4 groups, and each group gets 7 apples and 5 oranges.

Explanation

As the GCF of 28 and 20 is 4, the teacher can make 4 groups.

Now divide 28 and 20 by 4.

Each group gets 7 apples and 5 oranges.

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Problem 2

A school has 28 red chairs and 20 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?

Okay, lets begin

GCF of 28 and 20 2² = 4.

So each row will have 4 chairs.

Explanation

There are 28 red and 20 blue chairs. To find the total number of chairs in each row, we should find the GCF of 28 and 20.

There will be 4 chairs in each row.

Well explained 👍

Problem 3

A tailor has 28 meters of red ribbon and 20 meters of blue ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?

Okay, lets begin

For calculating the longest equal length, we have to calculate the GCF of 28 and 20

The GCF of 28 and 20 2² = 4.

The ribbon is 4 meters long.

Explanation

For calculating the longest length of the ribbon first we need to calculate the GCF of 28 and 20 which is 4.

The length of each piece of the ribbon will be 4 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 28 cm long and the other 20 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?

Okay, lets begin

The carpenter needs the longest piece of wood GCF of 28 and 20 2² = 4.

The longest length of each piece is 4 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 28 cm and 20 cm, respectively.

We have to find the GCF of 28 and 20, which is 4 cm.

The longest length of each piece is 4 cm.

Well explained 👍

FAQs on the Greatest Common Factor of 28 and 20

1.What is the LCM of 28 and 20?

The LCM of 28 and 20 is 140.

2.Is 20 divisible by 2?

Yes, 20 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 28 and 20 prime numbers?

No, 28 and 20 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 28 and 20

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.
  • Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 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 30 are 2, 3, and 5.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 15 is divided by 4, the remainder is 3 and the quotient is 3.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 28 and 20 is 140.

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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.