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100 LearnersLast updated on October 25, 2025
GCF of 30 and 6
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 30 and 6.
What is the GCF of 30 and 6?
The greatest common factor of 30 and 6 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 30 and 6?
To find the GCF of 30 and 6, a few methods are described below -
Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm
GCF of 30 and 6 by Using Listing of Factors
Steps to find the GCF of 30 and 6 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 6 = 1, 2, 3, 6.
Step 2: Now, identify the common factors of them Common factors of 30 and 6: 1, 2, 3, 6.
Step 3: Choose the largest factor The largest factor that both numbers have is 6.
The GCF of 30 and 6 is 6.
GCF of 30 and 6 Using Prime Factorization
To find the GCF of 30 and 6 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 6: 6 = 2 x 3.
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 6 is 6.
GCF of 30 and 6 Using Division Method or Euclidean Algorithm Method
Find the GCF of 30 and 6 using the division method or Euclidean Algorithm Method.
Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 30 by 6 30 ÷ 6 = 5 (quotient), The remainder is calculated as 30 − (6×5) = 0 Since the remainder is zero, the divisor is the GCF.
The GCF of 30 and 6 is 6.
Common Mistakes and How to Avoid Them in GCF of 30 and 6
Finding GCF of 30 and 6 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 indicates an 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 as 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 6 Examples
Problem 1
A teacher has 30 apples and 6 oranges. 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 30 and 6. GCF of 30 and 6 2 x 3 = 6.
There are 6 equal groups. 30 ÷ 6 = 5 6 ÷ 6 = 1.
There will be 6 groups, and each group gets 5 apples and 1 orange.
Explanation
As the GCF of 30 and 6 is 6, the teacher can make 6 groups.
Now divide 30 and 6 by 6.
Each group gets 5 apples and 1 orange.
Problem 2
A school has 30 red books and 6 blue books. They want to arrange them in rows with the same number of books in each row, using the largest possible number of books per row. How many books will be in each row?
GCF of 30 and 6 2 x 3 = 6.
So each row will have 6 books.
Explanation
There are 30 red and 6 blue books.
To find the total number of books in each row, we should find the GCF of 30 and 6.
There will be 6 books in each row.
Problem 3
A baker has 30 meters of red ribbon and 6 meters of green 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 30 and 6.
The GCF of 30 and 6 2 x 3 = 6.
The ribbon is 6 meters long.
Explanation
For calculating the longest length of the ribbon first, we need to calculate the GCF of 30 and 6, which is 6.
The length of each piece of the ribbon will be 6 meters.
Problem 4
A carpenter has two wooden planks, one 30 cm long and the other 6 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 30 and 6 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, 30 cm and 6 cm, respectively, we have to find the GCF of 30 and 6, which is 6 cm.
The longest length of each piece is 6 cm.
Problem 5
If the GCF of 30 and ‘a’ is 6, and the LCM is 90, find ‘a’.
The value of ‘a’ is 18.
Explanation
GCF x LCM = product of the numbers 6 × 90 = 30 × a 540 = 30a a = 540 ÷ 30 = 18
FAQs on the Greatest Common Factor of 30 and 6
1.What is the LCM of 30 and 6?
2.Is 30 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 6?
5.Are 30 and 6 prime numbers?
Important Glossaries for GCF of 30 and 6
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.
- 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 15 are 3 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 11 is divided by 4, the remainder is 3 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 3 and 4 is 12.
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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.
