100 LearnersLast updated on August 5th, 2025
GCF of 180 and 54
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 to schedule events. In this topic, we will learn about the GCF of 180 and 54.
What is the GCF of 180 and 54?
The greatest common factor of 180 and 54 is 18. 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 180 and 54?
To find the GCF of 180 and 54, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 180 and 54 by Using Listing of Factors
Steps to find the GCF of 180 and 54 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.
Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54.
Step 2: Now, identify the common factors of them Common factors of 180 and 54: 1, 2, 3, 6, 9, 18.
Step 3: Choose the largest factor
The largest factor that both numbers have is 18.
The GCF of 180 and 54 is 18.
GCF of 180 and 54 Using Prime Factorization
To find the GCF of 180 and 54 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 180: 180 = 2 x 2 x 3 x 3 x 5 = 2² x 3² x 5
Prime Factors of 54: 54 = 2 x 3 x 3 x 3 = 2 x 3³
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 3 x 3 = 2 x 3²
Step 3: Multiply the common prime factors 2 x 3² = 2 x 9 = 18.
The Greatest Common Factor of 180 and 54 is 18.
GCF of 180 and 54 Using Division Method or Euclidean Algorithm Method
Find the GCF of 180 and 54 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 180 by 54 180 ÷ 54 = 3 (quotient),
The remainder is calculated as 180 − (54 x 3) = 18
The remainder is 18, not zero, so continue the process
Step 2: Now divide the previous divisor (54) by the previous remainder (18)
Divide 54 by 18 54 ÷ 18 = 3 (quotient), remainder = 54 − (18 x 3) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 180 and 54 is 18.
Common Mistakes and How to Avoid Them in GCF of 180 and 54
Finding the GCF of 180 and 54 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 180, students may mention 50, 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 indicates an 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 180 and 54 Examples
Problem 1
A chef has 180 apples and 54 oranges. He wants to pack them into the largest possible equal groups. How many fruits will be in each group?
We should find the GCF of 180 and 54
GCF of 180 and 54 2 x 3² = 2 x 9 = 18.
There are 18 equal groups 180 ÷ 18 = 10
54 ÷ 18 = 3
There will be 18 groups, and each group gets 10 apples and 3 oranges.
Explanation
As the GCF of 180 and 54 is 18, the chef can make 18 groups. Now divide 180 and 54 by 18. Each group gets 10 apples and 3 oranges.
Problem 2
A company has 180 red chairs and 54 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?
GCF of 180 and 54 2 x 3² = 2 x 9 = 18.
So each row will have 18 chairs.
Explanation
There are 180 red and 54 blue chairs. To find the total number of chairs in each row, we should find the GCF of 180 and 54. There will be 18 chairs in each row.
Problem 3
A tailor has 180 meters of red fabric and 54 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 180 and 54
The GCF of 180 and 54 2 x 3² = 2 x 9 = 18.
The fabric is 18 meters long.
Explanation
For calculating the longest length of the fabric first, we need to calculate the GCF of 180 and 54, which is 18. The length of each piece of fabric will be 18 meters.
Problem 4
A carpenter has two wooden planks, one 180 cm long and the other 54 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 180 and 54 2 x 3² = 2 x 9 = 18.
The longest length of each piece is 18 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 180 cm and 54 cm, respectively. We have to find the GCF of 180 and 54, which is 18 cm. The longest length of each piece is 18 cm.
Problem 5
If the GCF of 180 and ‘b’ is 18, and the LCM is 540. Find ‘b’.
The value of ‘b’ is 54.
Explanation
GCF x LCM = product of the numbers 18 x 540 = 180 x b
9720 = 180b
b = 9720 ÷ 180 = 54
FAQs on the Greatest Common Factor of 180 and 54
1.What is the LCM of 180 and 54?
2.Is 180 divisible by 5?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 54?
5.Are 180 and 54 prime numbers?
6.How can children in India use numbers in everyday life to understand GCF of 180 and 54?
7.What are some fun ways kids in India can practice GCF of 180 and 54 with numbers?
8.What role do numbers and GCF of 180 and 54 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve GCF of 180 and 54 skills?
Important Glossary for GCF of 180 and 54
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18.
- 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 factors of 180 are 2, 3, and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 19 is divided by 5, the remainder is 4, and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 180 and 54 is 540.
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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.
