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101 LearnersLast updated on September 10, 2025
GCF of 30 and 54
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 30 and 54.
What is the GCF of 30 and 54?
The greatest common factor of 30 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 30 and 54?
To find the GCF of 30 and 54, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 30 and 54 by Using Listing of factors
Steps to find the GCF of 30 and 54 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30.
Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54.
Step 2: Now, identify the common factors of them Common factors of 30 and 54: 1, 2, 3, 6.
Step 3: Choose the largest factor The largest factor that both numbers have is 6. The GCF of 30 and 54 is 6.
GCF of 30 and 54 Using Prime Factorization
To find the GCF of 30 and 54 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime factors of 30: 30 = 2 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
Step 3: Multiply the common prime factors 2 x 3 = 6. The Greatest Common Factor of 30 and 54 is 6.
GCF of 30 and 54 Using Division Method or Euclidean Algorithm Method
Find the GCF of 30 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 54 by 30 54 ÷ 30 = 1 (quotient), The remainder is calculated as 54 − (30×1) = 24 The remainder is 24, not zero, so continue the process
Step 2: Now divide the previous divisor (30) by the previous remainder (24) Divide 30 by 24 30 ÷ 24 = 1 (quotient), remainder = 30 − (24×1) = 6
The remainder is 6, not zero, so continue the process
Step 3: Now divide the previous divisor (24) by the previous remainder (6) Divide 24 by 6 24 ÷ 6 = 4 (quotient), remainder = 24 − (6×4) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 30 and 54 is 6.
Common Mistakes and How to Avoid Them in GCF of 30 and 54
Finding GCF of 30 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 30, 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 30 and 54 Examples
Problem 1
A gardener has 30 rose bushes and 54 tulip bulbs. He wants to plant them in equal groups, using the largest possible number of plants in each group. How many plants will be in each group?
We should find GCF of 30 and 54 GCF of 30 and 54 2 x 3 = 6.
There are 6 equal groups 30 ÷ 6 = 5 54 ÷ 6 = 9
There will be 6 groups, and each group gets 5 rose bushes and 9 tulip bulbs.
Explanation
As the GCF of 30 and 54 is 6, the gardener can make 6 groups. Now divide 30 and 54 by 6. Each group gets 5 rose bushes and 9 tulip bulbs.
Problem 2
A farmer has 30 apples and 54 oranges. He wants to pack them in baskets with the same number of fruits in each basket, using the largest possible number of fruits per basket. How many fruits will be in each basket?
GCF of 30 and 54 2 x 3 = 6. So each basket will have 6 fruits.
Explanation
There are 30 apples and 54 oranges. To find the total number of fruits in each basket, we should find the GCF of 30 and 54. There will be 6 fruits in each basket.
Problem 3
A seamstress has 30 meters of fabric A and 54 meters of fabric B. 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 longest equal length, we have to calculate the GCF of 30 and 54 The GCF of 30 and 54 2 x 3 = 6. The fabric is 6 meters long.
Explanation
For calculating the longest length of the fabric first we need to calculate the GCF of 30 and 54 which is 6. The length of each piece of the fabric will be 6 meters.
Problem 4
A builder has two wooden beams, one 30 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 builder needs the longest piece of wood GCF of 30 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 beams, 30 cm and 54 cm, respectively. We have to find the GCF of 30 and 54, which is 6 cm. The longest length of each piece is 6 cm.
Problem 5
If the GCF of 30 and ‘b’ is 6, and the LCM is 270, find ‘b’.
The value of ‘b’ is 54.
Explanation
GCF x LCM = product of the numbers 6 × 270 = 30 × b 1620 = 30b b = 1620 ÷ 30 = 54
FAQs on the Greatest Common Factor of 30 and 54
1.What is the LCM of 30 and 54?
2.Is 30 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 54?
5.Are 30 and 54 prime numbers?
6.How can families in United States create number-rich environments to improve GCF of 30 and 54 skills?
7.What are some fun ways kids in United States can practice GCF of 30 and 54 with numbers?
8.What role do numbers and GCF of 30 and 54 play in helping children in United States develop problem-solving skills?
9.How can children in United States use numbers in everyday life to understand GCF of 30 and 54?
Important Glossaries for GCF of 30 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 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 30 are 2, 3, and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 54 is divided by 8, the remainder is 6.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 30 and 54 is 270.
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.
