GCF of 7 and 28
2026-02-28 21:40 Diff
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Last updated on September 18, 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 7 and 28.

What is the GCF of 7 and 28?

The greatest common factor of 7 and 28 is 7. 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 7 and 28?

To find the GCF of 7 and 28, a few methods are described below 

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

GCF of 7 and 28 by Using Listing of factors

Steps to find the GCF of 7 and 28 using the listing of factors

Step 1: Firstly, list the factors of each number

Factors of 7 = 1, 7.

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

Step 2: Now, identify the common factors of them Common factors of 7 and 28: 1, 7.

Step 3: Choose the largest factor The largest factor that both numbers have is 7. The GCF of 7 and 28 is 7.

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GCF of 7 and 28 Using Prime Factorization

To find the GCF of 7 and 28 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number

Prime Factors of 7: 7 = 7

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

Step 2: Now, identify the common prime factors The common prime factor is: 7

Step 3: Multiply the common prime factors 7 = 7 The Greatest Common Factor of 7 and 28 is 7.

GCF of 7 and 28 Using Division Method or Euclidean Algorithm Method

Find the GCF of 7 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 7 28 ÷ 7 = 4 (quotient), The remainder is calculated as 28 − (7×4) = 0 The remainder is zero, so the divisor will become the GCF.

The GCF of 7 and 28 is 7.

Common Mistakes and How to Avoid Them in GCF of 7 and 28

Finding GCF of 7 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 chef has 7 apples and 28 oranges. He 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 the GCF of 7 and 28 GCF of 7 and 28 7 = 7.

There are 7 equal groups 7 ÷ 7 = 1 28 ÷ 7 = 4

There will be 7 groups, and each group gets 1 apple and 4 oranges.

Explanation

As the GCF of 7 and 28 is 7, the chef can make 7 groups.

Now divide 7 and 28 by 7.

Each group gets 1 apple and 4 oranges.

Well explained 👍

Problem 2

A school has 7 green flags and 28 red flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?

Okay, lets begin

GCF of 7 and 28 7 = 7. So each row will have 7 flags.

Explanation

There are 7 green and 28 red flags.

To find the total number of flags in each row, we should find the GCF of 7 and 28.

There will be 7 flags in each row.

Well explained 👍

Problem 3

A tailor has 7 meters of yellow ribbon and 28 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 7 and 28

The GCF of 7 and 28 7 = 7.

The ribbon is 7 meters long.

Explanation

For calculating the longest length of the ribbon, first, we need to calculate the GCF of 7 and 28, which is 7.

The length of each piece of the ribbon will be 7 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 7 cm long and the other 28 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 7 and 28 7 = 7.

The longest length of each piece is 7 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 7 cm and 28 cm, respectively.

We have to find the GCF of 7 and 28, which is 7 cm.

The longest length of each piece is 7 cm.

Well explained 👍

Problem 5

If the GCF of 7 and ‘a’ is 7, and the LCM is 56, find ‘a’.

Okay, lets begin

The value of ‘a’ is 56.

Explanation

GCF x LCM = product of the numbers

7 × 56 = 7 × a

392 = 7a

a = 392 ÷ 7 = 56

Well explained 👍

FAQs on the Greatest Common Factor of 7 and 28

1.What is the LCM of 7 and 28?

The LCM of 7 and 28 is 28.

2.Is 7 divisible by 2?

No, 7 is not divisible by 2 because it is an odd 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 7 and 28 prime numbers?

No, 7 is a prime number, but 28 is not because it has more than two factors.

Important Glossaries for GCF of 7 and 28

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 7 are 1 and 7.
  • Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 7 are 7, 14, 21, 28, 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 factor of 28 is 7.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 9 is divided by 7, the remainder is 2 and the quotient is 1.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 7 and 28 is 28.
  • GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 7 and 28 is 7, 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.