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103 LearnersLast updated on September 11, 2025
GCF of 54 and 27
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 54 and 27.
What is the GCF of 54 and 27?
The greatest common factor of 54 and 27 is 27. The largest divisor of two or more numbers is called the GCF of the number. 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 54 and 27?
To find the GCF of 54 and 27, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 54 and 27 by Using Listing of Factors
Steps to find the GCF of 54 and 27 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54. Factors of 27 = 1, 3, 9, 27.
Step 2: Now, identify the common factors of them Common factors of 54 and 27: 1, 3, 9, 27.
Step 3: Choose the largest factor The largest factor that both numbers have is 27. The GCF of 54 and 27 is 27.
GCF of 54 and 27 Using Prime Factorization
To find the GCF of 54 and 27 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime Factors of each number Prime Factors of 54: 54 = 2 x 3 x 3 x 3 = 2 x 3³ Prime Factors of 27: 27 = 3 x 3 x 3 = 3³
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 54 and 27 is 27.
GCF of 54 and 27 Using Division Method or Euclidean Algorithm Method
Find the GCF of 54 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 54 by 27 54 ÷ 27 = 2 (quotient), The remainder is calculated as 54 − (27×2) = 0
The remainder is zero, so the divisor will become the GCF. The GCF of 54 and 27 is 27.
Common Mistakes and How to Avoid Them in GCF of 54 and 27
Finding GCF of 54 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 54, students may mention 8, 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 54 and 27 Examples
Problem 1
A bakery has 54 cupcakes and 27 muffins. They want to arrange them on trays with the same number of items on each tray, using the largest possible number of items per tray. How many items will be on each tray?
We should find the GCF of 54 and 27 GCF of 54 and 27 3³ = 27.
There are 27 equal items per tray 54 ÷ 27 = 2 27 ÷ 27 = 1
There will be 2 trays, and each tray gets 2 cupcakes and 1 muffin.
Explanation
As the GCF of 54 and 27 is 27, the bakery can make 27 items per tray. Now divide 54 and 27 by 27. Each tray gets 2 cupcakes and 1 muffin.
Problem 2
A decorator has 54 red balloons and 27 blue balloons. They want to arrange them in clusters with the same number of balloons in each cluster, using the largest possible number of balloons per cluster. How many balloons will be in each cluster?
GCF of 54 and 27
3³ = 27.
So each cluster will have 27 balloons.
Explanation
There are 54 red and 27 blue balloons. To find the total number of balloons in each cluster, we should find the GCF of 54 and 27. There will be 27 balloons in each cluster.
Problem 3
A florist has 54 meters of red ribbon and 27 meters of blue ribbon. She wants to cut both ribbons 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 54 and 27
The GCF of 54 and 27 3³ = 27. The ribbon is 27 meters long.
Explanation
For calculating the longest length of the ribbon first, we need to calculate the GCF of 54 and 27, which is 27. The length of each piece of the ribbon will be 27 meters.
Problem 4
A carpenter has two wooden planks, one 54 cm long and the other 27 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 54 and 27 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, 54 cm and 27 cm, respectively, we have to find the GCF of 54 and 27, which is 27 cm. The longest length of each piece is 27 cm.
Problem 5
If the GCF of 54 and ‘b’ is 27, and the LCM is 162. Find ‘b’.
The value of ‘b’ is 81.
Explanation
GCF x LCM = product of the numbers
27 × 162 = 54 × b
4374 = 54b
b = 4374 ÷ 54 = 81
FAQs on the Greatest Common Factor of 54 and 27
1.What is the LCM of 54 and 27?
2.Is 54 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 27?
5.Are 54 and 27 prime numbers?
Important Glossaries for GCF of 54 and 27
- 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 27 are 27, 54, 81, 108, 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 54 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 54 is divided by 7, the remainder is 5 and the quotient is 7.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 54 and 27 is 162.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 54 and 27 is 27, as it is their largest common factor that divides the numbers completely.
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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.
