BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon101 Learners

Last updated on August 5th, 2025

Math Whiteboard Illustration

GCF of 36 and 27

Professor Greenline Explaining Math Concepts

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.

GCF of 36 and 27 for US Students
Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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
Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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.

Max Pointing Out Common Math Mistakes

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

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Listing Incorrect Factors

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

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

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Choosing the Wrong Common Factor

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

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

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Forgetting to Include 1 as a Factor

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

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

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Using Multiples Instead of Factors

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

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

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Assuming GCF is Always an Even Number

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

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.

arrow-right
Max from BrightChamps Saying "Hey"
Hey!

Greatest Common Factor of 36 and 27 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

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?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"
Okay, lets begin

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.

Max from BrightChamps Praising Clear Math Explanations
Well explained 👍
Max, the Girl Character from BrightChamps

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?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"
Okay, lets begin

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.

Max from BrightChamps Praising Clear Math Explanations
Well explained 👍
Max, the Girl Character from BrightChamps

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?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"
Okay, lets begin

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.

Max from BrightChamps Praising Clear Math Explanations
Well explained 👍
Max, the Girl Character from BrightChamps

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?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"
Okay, lets begin

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.

Max from BrightChamps Praising Clear Math Explanations
Well explained 👍
Max, the Girl Character from BrightChamps

Problem 5

If the GCF of 36 and ‘b’ is 9, and the LCM is 108, find ‘b’.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"
Okay, lets begin

The value of ‘b’ is 27.

Explanation

GCF x LCM = product of the numbers 9 × 108 = 36 × b

972 = 36b

b = 972 ÷ 36 = 27

Max from BrightChamps Praising Clear Math Explanations
Well explained 👍
Ray Thinking Deeply About Math Problems

FAQs on the Greatest Common Factor of 36 and 27

1.What is the LCM of 36 and 27?

The LCM of 36 and 27 is 108.

Math FAQ Answers Dropdown Arrow

2.Is 36 divisible by 3?

Yes, 36 is divisible by 3 because the sum of its digits (3 + 6) is 9, which is divisible by 3.

Math FAQ Answers Dropdown Arrow

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.

Math FAQ Answers Dropdown Arrow

4.What is the prime factorization of 27?

The prime factorization of 27 is 3³.

Math FAQ Answers Dropdown Arrow

5.Are 36 and 27 prime numbers?

No, 36 and 27 are not prime numbers because both of them have more than two factors.

Math FAQ Answers Dropdown Arrow

6.How can children in United States use numbers in everyday life to understand GCF of 36 and 27?

Numbers appear everywhere—from counting money to measuring ingredients. Kids in United States see how GCF of 36 and 27 helps solve real problems, making numbers meaningful beyond the classroom.

Math FAQ Answers Dropdown Arrow

7.What are some fun ways kids in United States can practice GCF of 36 and 27 with numbers?

Games like board games, sports scoring, or even cooking help children in United States use numbers naturally. These activities make practicing GCF of 36 and 27 enjoyable and connected to their world.

Math FAQ Answers Dropdown Arrow

8.What role do numbers and GCF of 36 and 27 play in helping children in United States develop problem-solving skills?

Working with numbers through GCF of 36 and 27 sharpens reasoning and critical thinking, preparing kids in United States for challenges inside and outside the classroom.

Math FAQ Answers Dropdown Arrow

9.How can families in United States create number-rich environments to improve GCF of 36 and 27 skills?

Families can include counting chores, measuring recipes, or budgeting allowances, helping children connect numbers and GCF of 36 and 27 with everyday activities.

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

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.
Math Teacher Background Image
Math Teacher Image

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.

Max, the Girl Character from BrightChamps

Fun Fact

: She loves to read number jokes and games.

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
UAE - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom