102 LearnersLast updated on July 28th, 2025
GCF of 36 and 81
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 36 and 81.
What is the GCF of 36 and 81?
The greatest common factor of 36 and 81 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 81?
To find the GCF of 36 and 81, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 36 and 81 by Using Listing of factors
Steps to find the GCF of 36 and 81 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 81 = 1, 3, 9, 27, 81.
Step 2: Now, identify the common factors of them Common factors of 36 and 81: 1, 3, 9.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 9.
The GCF of 36 and 81 is 9.
GCF of 36 and 81 Using Prime Factorization
To find the GCF of 36 and 81 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number:
Prime Factors of 36: 36 = 2×2×3×3 = 2²×3²
Prime Factors of 81: 81 = 3×3×3×3 = 3⁴
Step 2: Now, identify the common prime factors.
The common prime factors are: 3×3 = 3²
Step 3: Multiply the common prime factors 3² = 9.
The Greatest Common Factor of 36 and 81 is 9.
GCF of 36 and 81 Using Division Method or Euclidean Algorithm Method
Find the GCF of 36 and 81 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number.
Here, divide 81 by 36 81 ÷ 36 = 2 (quotient),
The remainder is calculated as 81 − (36×2) = 9
The remainder is 9, not zero, so continue the process
Step 2: Now divide the previous divisor (36) by the previous remainder (9)
Divide 36 by 9 36 ÷ 9 = 4 (quotient), remainder = 36 − (9×4) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 36 and 81 is 9.
Common Mistakes and How to Avoid Them in GCF of 36 and 81
Finding GCF of 36 and 81 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 25 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 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 81 Examples
Problem 1
A gardener has 36 roses and 81 lilies. She wants to plant them in rows with an equal number of flowers. What is the largest number of flowers she can have in each row?
We should find the GCF of 36 and 81 GCF of 36 and 81
3² = 9.
She can plant 9 flowers in each row.
36 ÷ 9 = 4
81 ÷ 9 = 9
There will be 9 flowers in each row, with 4 rows of roses and 9 rows of lilies.
Explanation
As the GCF of 36 and 81 is 9, the gardener can have 9 flowers in each row.
Now divide 36 and 81 by 9.
There will be 4 rows of roses and 9 rows of lilies, each with 9 flowers.
Problem 2
A baker has 36 chocolate muffins and 81 vanilla muffins. He wants to package them into boxes with the same number of muffins. What is the largest number of muffins that can be in each box?
GCF of 36 and 81 3² = 9. So each box will have 9 muffins.
Explanation
There are 36 chocolate and 81 vanilla muffins.
To find the total number of muffins in each box, we should find the GCF of 36 and 81.
There will be 9 muffins in each box.
Problem 3
A tailor has 36 meters of fabric for dresses and 81 meters for shirts. 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 81
The GCF of 36 and 81
3² = 9.
The fabric is 9 meters long.
Explanation
For calculating the longest length of the fabric first we need to calculate the GCF of 36 and 81 which is 9.
The length of each piece of fabric will be 9 meters.
Problem 4
A carpenter has two wooden planks, one 36 cm long and the other 81 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 81
3² = 9.
The longest length of each piece is 9 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 36 cm and 81 cm, respectively.
We have to find the GCF of 36 and 81, 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 324. Find ‘b’.
The value of ‘b’ is 81.
Explanation
GCF × LCM = product of the numbers
9 × 324 = 36 × b
2916 = 36b
b = 2916 ÷ 36 = 81
FAQs on the Greatest Common Factor of 36 and 81
1.What is the LCM of 36 and 81?
2.Is 81 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 81?
5.Are 36 and 81 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 36 and 81?
7.What are some fun ways kids in United States can practice GCF of 36 and 81 with numbers?
8.What role do numbers and GCF of 36 and 81 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 81 skills?
Important Glossaries for GCF of 36 and 81
- 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 9 are 9, 18, 27, 36, 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 36 are 2 and 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.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 36 and 81 is 9, 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.
