103 LearnersLast updated on August 12th, 2025
GCF of 27 and 81
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 27 and 81.
What is the GCF of 27 and 81?
The greatest common factor of 27 and 81 is 27. 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 27 and 81?
To find the GCF of 27 and 81, a few methods are described below: -
- Listing Factors
- Prime Factorization
- Long Division Method / Euclidean Algorithm
GCF of 27 and 81 by Using Listing of Factors
Steps to find the GCF of 27 and 81 using the listing of factors:
Step 1: Firstly, list the factors of each number. Factors of 27 = 1, 3, 9, 27. Factors of 81 = 1, 3, 9, 27, 81.
Step 2: Now, identify the common factors of them. Common factors of 27 and 81: 1, 3, 9, 27.
Step 3: Choose the largest factor. The largest factor that both numbers have is 27. The GCF of 27 and 81 is 27.
GCF of 27 and 81 Using Prime Factorization
To find the GCF of 27 and 81 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number. Prime Factors of 27: 27 = 3 x 3 x 3 = 3³ Prime Factors of 81: 81 = 3 x 3 x 3 x 3 = 3⁴
Step 2: Now, identify the common prime factors. The common prime factors are: 3 x 3 x 3 = 3³
Step 3: Multiply the common prime factors. 3³ = 27. The Greatest Common Factor of 27 and 81 is 27.
GCF of 27 and 81 Using Division Method or Euclidean Algorithm Method
Find the GCF of 27 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 27. 81 ÷ 27 = 3 (quotient), The remainder is calculated as 81 − (27×3) = 0.
Since the remainder is zero, the divisor will become the GCF. The GCF of 27 and 81 is 27.
Common Mistakes and How to Avoid Them in GCF of 27 and 81
Finding the GCF of 27 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 27, 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 with 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 27 and 81 Examples
Problem 1
A teacher has 27 notebooks and 81 pencils. 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 27 and 81. GCF of 27 and 81: 3³ = 27.
There are 27 equal groups. 27 ÷ 27 = 1 81 ÷ 27 = 3
There will be 27 groups, and each group gets 1 notebook and 3 pencils.
Explanation
As the GCF of 27 and 81 is 27, the teacher can make 27 groups. Now divide 27 and 81 by 27. Each group gets 1 notebook and 3 pencils.
Problem 2
A school has 27 red flags and 81 blue flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?
GCF of 27 and 81: 3³ = 27. So each row will have 27 flags.
Explanation
There are 27 red and 81 blue flags. To find the total number of flags in each row, we should find the GCF of 27 and 81. There will be 27 flags in each row.
Problem 3
A tailor has 27 meters of red fabric and 81 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 27 and 81. The GCF of 27 and 81: 3³ = 27. The fabric is 27 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 27 and 81, which is 27. The length of each piece of fabric will be 27 meters.
Problem 4
A carpenter has two wooden planks, one 27 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 27 and 81: 3³ = 27. The longest length of each piece is 27 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 27 cm and 81 cm, respectively, we have to find the GCF of 27 and 81, which is 27 cm. The longest length of each piece is 27 cm.
Problem 5
If the GCF of 27 and ‘a’ is 27, and the LCM is 81. Find ‘a’.
The value of ‘a’ is 81.
Explanation
GCF x LCM = product of the numbers
27 × 81 = 27 × a
2187 = 27a
a = 2187 ÷ 27 = 81
FAQs on the Greatest Common Factor of 27 and 81
1.What is the LCM of 27 and 81?
2.Is 27 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 81?
5.Are 27 and 81 prime numbers?
6.How can children in United Kingdom use numbers in everyday life to understand GCF of 27 and 81?
7.What are some fun ways kids in United Kingdom can practice GCF of 27 and 81 with numbers?
8.What role do numbers and GCF of 27 and 81 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve GCF of 27 and 81 skills?
Important Glossaries for GCF of 27 and 81
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 27 are 1, 3, 9, and 27.
- 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, 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 factor of 27 is 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 27 and 81 is 81.
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.
