101 LearnersLast updated on August 1st, 2025
GCF of 60 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 schedule events. In this topic, we will learn about the GCF of 60 and 54.
What is the GCF of 60 and 54?
The greatest common factor of 60 and 54 is 6. 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 60 and 54?
To find the GCF of 60 and 54, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 60 and 54 by Using Listing of Factors
Steps to find the GCF of 60 and 54 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54.
Step 2: Now, identify the common factors of them Common factors of 60 and 54: 1, 2, 3, 6.
Step 3: Choose the largest factor
The largest factor that both numbers have is 6.
The GCF of 60 and 54 is 6.
GCF of 60 and 54 Using Prime Factorization
To find the GCF of 60 and 54 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 60: 60 = 2 x 2 x 3 x 5 = 2² x 3 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 = 2 x 3
Step 3: Multiply the common prime factors 2 x 3 = 6.
The Greatest Common Factor of 60 and 54 is 6.
GCF of 60 and 54 Using Division Method or Euclidean Algorithm Method
Find the GCF of 60 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 60 by 54 60 ÷ 54 = 1 (quotient),
The remainder is calculated as 60 − (54×1) = 6
The remainder is 6, not zero, so continue the process
Step 2: Now divide the previous divisor (54) by the previous remainder (6)
Divide 54 by 6 54 ÷ 6 = 9 (quotient), remainder = 54 − (6×9) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 60 and 54 is 6.
Common Mistakes and How to Avoid Them in GCF of 60 and 54
Finding the GCF of 60 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 60, 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 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 60 and 54 Examples
Problem 1
A teacher has 60 markers and 54 notebooks. 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 60 and 54 GCF of 60 and 54 2 x 3 = 6.
There are 6 equal groups 60 ÷ 6 = 10 54 ÷ 6 = 9
There will be 6 groups, and each group gets 10 markers and 9 notebooks.
Explanation
As the GCF of 60 and 54 is 6, the teacher can make 6 groups. Now divide 60 and 54 by 6. Each group gets 10 markers and 9 notebooks.
Problem 2
A school has 60 whiteboards and 54 projectors. They want to arrange them in rows with the same number of items in each row, using the largest possible number of items per row. How many items will be in each row?
GCF of 60 and 54 2 x 3 = 6.
So, each row will have 6 items.
Explanation
There are 60 whiteboards and 54 projectors. To find the total number of items in each row, we should find the GCF of 60 and 54. There will be 6 items in each row.
Problem 3
A tailor has 60 meters of green fabric and 54 meters of yellow 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 60 and 54
The GCF of 60 and 54 2 x 3 = 6.
The fabric pieces will be 6 meters long.
Explanation
For calculating the longest length of the fabric pieces, first we need to calculate the GCF of 60 and 54, which is 6. The length of each fabric piece will be 6 meters.
Problem 4
A carpenter has two wooden planks, one 60 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 60 and 54 2 x 3 = 6.
The longest length of each piece is 6 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 60 cm and 54 cm, respectively, we have to find the GCF of 60 and 54, which is 6 cm. The longest length of each piece is 6 cm.
Problem 5
If the GCF of 60 and ‘b’ is 6, and the LCM is 540. Find ‘b’.
The value of ‘b’ is 54.
Explanation
GCF x LCM = product of the numbers 6 × 540 = 60 × b
3240 = 60b
b = 3240 ÷ 60 = 54
FAQs on the Greatest Common Factor of 60 and 54
1.What is the LCM of 60 and 54?
2.Is 60 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 54?
5.Are 60 and 54 prime numbers?
6.How can children in Philippines use numbers in everyday life to understand GCF of 60 and 54?
7.What are some fun ways kids in Philippines can practice GCF of 60 and 54 with numbers?
8.What role do numbers and GCF of 60 and 54 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve GCF of 60 and 54 skills?
Important Glossaries for GCF of 60 and 54
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 6 are 1, 2, 3, and 6.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, 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 30 are 2, 3, and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 4, the remainder is 2 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 60 and 54 is 540.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 60 and 54 is 6, 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.
