105 LearnersLast updated on August 5th, 2025
GCF of 36 and 27
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 schedule events. In this topic, we will learn about the GCF of 36 and 27.
What is the GCF of 36 and 27?
The greatest common factor of 36 and 27 is 9. 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 27?
To find the GCF of 36 and 27, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 36 and 27 by Using Listing of Factors
Steps to find the GCF of 36 and 27 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 27 = 1, 3, 9, 27.
Step 2: Now, identify the common factors Common factors of 36 and 27: 1, 3, 9.
Step 3: Choose the largest factor
The largest factor that both numbers have is 9.
The GCF of 36 and 27 is 9.
GCF of 36 and 27 Using Prime Factorization
To find the GCF of 36 and 27 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 27: 27 = 3 x 3 x 3 = 3³
Step 2: Identify the common prime factors
The common prime factors are: 3 x 3 = 3²
Step 3: Multiply the common prime factors 3² = 9.
The Greatest Common Factor of 36 and 27 is 9.
GCF of 36 and 27 Using Division Method or Euclidean Algorithm Method
Find the GCF of 36 and 27 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 27 36 ÷ 27 = 1 (quotient),
The remainder is calculated as 36 − (27 x 1) = 9
The remainder is 9, not zero, so continue the process
Step 2: Now divide the previous divisor (27) by the previous remainder (9)
Divide 27 by 9 27 ÷ 9 = 3 (quotient), remainder = 27 − (9 x 3) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 36 and 27 is 9.
Common Mistakes and How to Avoid Them in GCF of 36 and 27
Finding GCF of 36 and 27 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 36, 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 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 36 and 27 Examples
Problem 1
A chef has 36 apples and 27 oranges. She wants to create fruit baskets with the largest number of fruits in each basket, ensuring each basket is identical. How many fruits will be in each basket?
We should find the GCF of 36 and 27.
GCF of 36 and 27: 3² = 9.
There are 9 equal groups. 36 ÷ 9 = 4 27 ÷ 9 = 3
There will be 9 baskets, and each basket gets 4 apples and 3 oranges.
Explanation
As the GCF of 36 and 27 is 9, the chef can make 9 baskets. Now divide 36 and 27 by 9. Each basket gets 4 apples and 3 oranges.
Problem 2
A company has 36 brochures and 27 flyers. They want to distribute them in packets with the same number of items in each packet, using the largest possible number of items per packet. How many items will be in each packet?
GCF of 36 and 27: 3² = 9.
So each packet will have 9 items.
Explanation
There are 36 brochures and 27 flyers. To find the total number of items in each packet, we should find the GCF of 36 and 27. There will be 9 items in each packet.
Problem 3
A gardener has 36 tulip bulbs and 27 daffodil bulbs. She wants to plant them in rows with the same number of bulbs in each row, using the longest possible row length. How many bulbs should be in each row?
For calculating the longest equal row length, we have to calculate the GCF of 36 and 27.
The GCF of 36 and 27: 3² = 9.
Each row is 9 bulbs long.
Explanation
For calculating the longest row length, we first need to calculate the GCF of 36 and 27, which is 9. The length of each row of bulbs will be 9.
Problem 4
A builder has two steel rods, one 36 cm long and the other 27 cm long. He wants to cut them into the longest possible equal pieces, without any steel left over. What should be the length of each piece?
The builder needs the longest piece of steel.
GCF of 36 and 27: 3² = 9.
The longest length of each piece is 9 cm.
Explanation
To find the longest length of each piece of the two steel rods, 36 cm and 27 cm, respectively, we have to find the GCF of 36 and 27, which is 9 cm. The longest length of each piece is 9 cm.
Problem 5
If the GCF of 36 and ‘b’ is 9, and the LCM is 108, find ‘b’.
The value of ‘b’ is 27.
Explanation
GCF x LCM = product of the numbers 9 × 108 = 36 × b
972 = 36b
b = 972 ÷ 36 = 27
FAQs on the Greatest Common Factor of 36 and 27
1.What is the LCM of 36 and 27?
2.Is 36 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 27?
5.Are 36 and 27 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 36 and 27?
7.What are some fun ways kids in United States can practice GCF of 36 and 27 with numbers?
8.What role do numbers and GCF of 36 and 27 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve GCF of 36 and 27 skills?
Important Glossaries for GCF of 36 and 27
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 15, 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 27 are 3.
- 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 27 is 108.
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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.
