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102 LearnersLast updated on September 19, 2025
GCF of 36 and 28
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 36 and 28.
What is the GCF of 36 and 28?
The greatest common factor of 36 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 36 and 28?
To find the GCF of 36 and 28, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 36 and 28 by Using Listing of factors
Steps to find the GCF of 36 and 28 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.
Factors of 28 = 1, 2, 4, 7, 14, 28.
Step 2: Now, identify the common factors of them Common factors of 36 and 28: 1, 2, 4.
Step 3: Choose the largest factor The largest factor that both numbers have is 4. The GCF of 36 and 28 is 4.
GCF of 36 and 28 Using Prime Factorization
To find the GCF of 36 and 28 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 36 : 36 = 2 x 2 x 3 x 3 = 2² x 3²
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: 2 x 2 = 2²
Step 3: Multiply the common prime factors 2² = 4. The Greatest Common Factor of 36 and 28 is 4.
GCF of 36 and 28 Using Division Method or Euclidean Algorithm Method
Find the GCF of 36 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 36 by 28 36 ÷ 28 = 1 (quotient),
The remainder is calculated as 36 − (28×1) = 8
The remainder is 8, not zero, so continue the process
Step 2: Now divide the previous divisor (28) by the previous remainder (8)
Divide 28 by 8 28 ÷ 8 = 3 (quotient), remainder = 28 − (8×3) = 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 36 and 28 is 4.
Common Mistakes and How to Avoid Them in GCF of 36 and 28
Finding the GCF of 36 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 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 tells about the incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse between 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 that 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 36 and 28 Examples
Problem 1
A gardener has 36 plants and 28 pots. 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?
We should find the GCF of 36 and 28 GCF of 36 and 28 2² = 4.
There are 4 equal groups 36 ÷ 4 = 9 28 ÷ 4 = 7
There will be 4 groups, and each group gets 9 plants and 7 pots.
Explanation
As the GCF of 36 and 28 is 4, the gardener can make 4 groups.
Now divide 36 and 28 by 4.
Each group gets 9 plants and 7 pots.
Problem 2
A school fundraiser has 36 cookies and 28 brownies. They want to arrange them in trays with the same number of treats in each tray, using the largest possible number of treats per tray. How many treats will be in each tray?
GCF of 36 and 28 2² = 4.
So each tray will have 4 treats.
Explanation
There are 36 cookies and 28 brownies.
To find the total number of treats in each tray, we should find the GCF of 36 and 28.
There will be 4 treats in each tray.
Problem 3
A tailor has 36 meters of red fabric and 28 meters of blue fabric. She wants to cut both fabrics into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 36 and 28
The GCF of 36 and 28 2² = 4.
The fabric is 4 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 36 and 28, which is 4.
The length of each piece of the fabric will be 4 meters.
Problem 4
A carpenter has two wooden planks, one 36 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?
The carpenter needs the longest piece of wood GCF of 36 and 28 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, 36 cm and 28 cm, respectively, we have to find the GCF of 36 and 28, which is 4 cm.
The longest length of each piece is 4 cm.
Problem 5
If the GCF of 36 and ‘b’ is 4, and the LCM is 252. Find ‘b’.
The value of ‘b’ is 28.
Explanation
GCF x LCM = product of the numbers
4 × 252 = 36 × b
1008 = 36b
b = 1008 ÷ 36 = 28
FAQs on the Greatest Common Factor of 36 and 28
1.What is the LCM of 36 and 28?
2.Is 36 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 28?
5.Are 36 and 28 prime numbers?
Important Glossaries for GCF of 36 and 28
- 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 28 are 2 and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 36 and 28 is 252.
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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.
