107 LearnersLast updated on 14 August 2025
GCF of 28 and 72
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 72.
What is the GCF of 28 and 72?
The greatest common factor of 28 and 72 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 72?
To find the GCF of 28 and 72, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 28 and 72 by Using Listing of Factors
Steps to find the GCF of 28 and 72 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 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
Step 2: Now, identify the common factors of them Common factors of 28 and 72: 1, 2, 4.
Step 3: Choose the largest factor The largest factor that both numbers have is 4. The GCF of 28 and 72 is 4.
GCF of 28 and 72 Using Prime Factorization
To find the GCF of 28 and 72 using the 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 72: 72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²
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 72 is 4.
GCF of 28 and 72 Using Division Method or Euclidean Algorithm Method
Find the GCF of 28 and 72 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 72 by 28 72 ÷ 28 = 2 (quotient), The remainder is calculated as 72 - (28 x 2) = 16 The remainder is 16, not zero, so continue the process
Step 2: Now divide the previous divisor (28) by the previous remainder (16) Divide 28 by 16 28 ÷ 16 = 1 (quotient), remainder = 28 - (16 x 1) = 12
Step 3: Divide 16 by 12 16 ÷ 12 = 1 (quotient), remainder = 16 - (12 x 1) = 4
Step 4: Divide 12 by 4 12 ÷ 4 = 3 (quotient), remainder = 12 - (4 x 3) = 0 The remainder is zero, the divisor will become the GCF. The GCF of 28 and 72 is 4.
Common Mistakes and How to Avoid Them in GCF of 28 and 72
Finding the GCF of 28 and 72 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 28, students may mention 10, 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 indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse 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 28 and 72 Examples
Problem 1
A gardener has 28 tulips and 72 roses. She wants to plant them in equal rows with the largest number of flowers per row. How many flowers will be in each row?
We should find the GCF of 28 and 72 GCF of 28 and 72 2² = 4.
There are 4 equal rows 28 ÷ 4 = 7 72 ÷ 4 = 18
There will be 4 rows, and each row gets 7 tulips and 18 roses.
Explanation
As the GCF of 28 and 72 is 4, the gardener can make 4 rows. Now divide 28 and 72 by 4. Each row gets 7 tulips and 18 roses.
Problem 2
A chef has 28 apples and 72 oranges. He wants to make fruit baskets with the same number of fruits in each basket, using the largest possible number of fruits per basket. How many fruits will be in each basket?
GCF of 28 and 72 2² = 4. So each basket will have 4 fruits.
Explanation
There are 28 apples and 72 oranges. To find the total number of fruits in each basket, we should find the GCF of 28 and 72. There will be 4 fruits in each basket.
Problem 3
A painter has 28 meters of red paint and 72 meters of blue paint. She wants to divide both types of paint into segments of equal length, using the longest possible length. What should be the length of each segment?
For calculating the longest equal length, we have to calculate the GCF of 28 and 72 The GCF of 28 and 72 2² = 4. The paint is 4 meters long.
Explanation
For calculating the longest length of the paint first, we need to calculate the GCF of 28 and 72, which is 4. The length of each segment of the paint will be 4 meters.
Problem 4
A carpenter has two wooden planks, one 28 cm long and the other 72 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 28 and 72 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 72 cm, respectively, we have to find the GCF of 28 and 72, which is 4 cm. The longest length of each piece is 4 cm.
Problem 5
If the GCF of 28 and ‘b’ is 4, and the LCM is 504. Find ‘b’.
The value of ‘b’ is 72.
Explanation
GCF x LCM = product of the numbers
4 x 504 = 28 x b
2016 = 28b
b = 2016 ÷ 28 = 72
FAQs on the Greatest Common Factor of 28 and 72
1.What is the LCM of 28 and 72?
2.Is 28 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 72?
5.Are 28 and 72 prime numbers?
6.How can children in India use numbers in everyday life to understand GCF of 28 and 72?
7.What are some fun ways kids in India can practice GCF of 28 and 72 with numbers?
8.What role do numbers and GCF of 28 and 72 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve GCF of 28 and 72 skills?
Important Glossaries for GCF of 28 and 72
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.
- Prime Factorization: It is the process of expressing a number as the product of its prime factors. For example, the prime factorization of 18 is 2 x 3².
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 35 is divided by 6, the remainder is 5, and the quotient is 5.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 28 and 72 is 504.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 28 and 72 will be 4, as it is their largest common factor that divides the numbers completely.
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.
