103 LearnersLast updated on August 11th, 2025
GCF of 54 and 42
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 42.
What is the GCF of 54 and 42?
The greatest common factor of 54 and 42 is 6. 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 54 and 42?
To find the GCF of 54 and 42, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 54 and 42 by Using Listing of factors
Steps to find the GCF of 54 and 42 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 42 = 1, 2, 3, 6, 7, 14, 21, 42.
Step 2: Now, identify the common factors of them Common factors of 54 and 42: 1, 2, 3, 6.
Step 3: Choose the largest factor The largest factor that both numbers have is 6. The GCF of 54 and 42 is 6.
GCF of 54 and 42 Using Prime Factorization
To find the GCF of 54 and 42 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 42: 42 = 2 x 3 x 7
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 3 = 6
Step 3: Multiply the common prime factors 2 x 3 = 6. The Greatest Common Factor of 54 and 42 is 6.
GCF of 54 and 42 Using Division Method or Euclidean Algorithm Method
Find the GCF of 54 and 42 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 42 54 ÷ 42 = 1 (quotient), The remainder is calculated as 54 − (42×1) = 12.
The remainder is 12, not zero, so continue the process
Step 2: Now divide the previous divisor (42) by the previous remainder (12) Divide 42 by 12 42 ÷ 12 = 3 (quotient), remainder = 42 − (12×3) = 6.
Step 3: Now, divide the previous divisor (12) by the previous remainder (6) 12 ÷ 6 = 2 (quotient), remainder = 12 − (6×2) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 54 and 42 is 6.
Common Mistakes and How to Avoid Them in GCF of 54 and 42
Finding the GCF of 54 and 42 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 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 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 54 and 42 Examples
Problem 1
A farmer has 54 apples and 42 oranges. He wants to pack them into boxes with the largest number of each fruit in every box. How many pieces of fruit will each box contain?
We should find the GCF of 54 and 42 GCF of 54 and 42 is 6. There are 6 equal groups. 54 ÷ 6 = 9 42 ÷ 6 = 7 There will be 6 boxes, and each box gets 9 apples and 7 oranges.
Explanation
As the GCF of 54 and 42 is 6, the farmer can make 6 boxes. Now divide 54 and 42 by 6. Each box gets 9 apples and 7 oranges.
Problem 2
A concert hall has 54 chairs in one section and 42 chairs in another section. 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 54 and 42 is 6. So each row will have 6 chairs.
Explanation
There are 54 chairs in one section and 42 chairs in another section. To find the total number of chairs in each row, we should find the GCF of 54 and 42. There will be 6 chairs in each row.
Problem 3
A ribbon supplier has 54 meters of red ribbon and 42 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 42. The GCF of 54 and 42 is 6. The ribbon pieces are 6 meters long.
Explanation
For calculating the longest length of the ribbon first, we need to calculate the GCF of 54 and 42, which is 6. The length of each piece of the ribbon will be 6 meters.
Problem 4
A carpenter has two wooden planks, one 54 cm long and the other 42 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 42 is 6. The longest length of each piece is 6 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 54 cm and 42 cm, respectively, we have to find the GCF of 54 and 42, which is 6 cm. The longest length of each piece is 6 cm.
Problem 5
If the GCF of 54 and ‘a’ is 6, and the LCM is 378. Find ‘a’.
The value of ‘a’ is 42.
Explanation
GCF x LCM = product of the numbers 6 × 378 = 54 × a 2268 = 54a a = 2268 ÷ 54 = 42
FAQs on the Greatest Common Factor of 54 and 42
1.What is the LCM of 54 and 42?
2.Is 54 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 42?
5.Are 54 and 42 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 54 and 42?
7.What are some fun ways kids in United States can practice GCF of 54 and 42 with numbers?
8.What role do numbers and GCF of 54 and 42 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 54 and 42 skills?
Important Glossaries for GCF of 54 and 42
- 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, 15, 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 21 are 3 and 7.
- 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 54 and 42 is 378.
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.
