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104 LearnersLast updated on August 11, 2025
GCF of 12 and 30
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 12 and 30.
What is the GCF of 12 and 30?
The greatest common factor of 12 and 30 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 12 and 30?
To find the GCF of 12 and 30, a few methods are described below - Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm
GCF of 12 and 30 by Using Listing of factors
Steps to find the GCF of 12 and 30 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 12 = 1, 2, 3, 4, 6, 12.
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30.
Step 2: Now, identify the common factors Common factors of 12 and 30: 1, 2, 3, 6.
Step 3: Choose the largest factor The largest factor that both numbers have is 6. The GCF of 12 and 30 is 6.
GCF of 12 and 30 Using Prime Factorization
To find the GCF of 12 and 30 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 12: 12 = 2 × 2 × 3 = 2² × 3
Prime Factors of 30: 30 = 2 × 3 × 5
Step 2: Now, identify the common prime factors The common prime factors are: 2 × 3
Step 3: Multiply the common prime factors 2 × 3 = 6. The Greatest Common Factor of 12 and 30 is 6.
GCF of 12 and 30 Using Division Method or Euclidean Algorithm Method
Find the GCF of 12 and 30 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 12 30 ÷ 12 = 2 (quotient), The remainder is calculated as 30 − (12×2) = 6 The remainder is 6, not zero, so continue the process
Step 2: Now divide the previous divisor (12) by the previous remainder (6) Divide 12 by 6 12 ÷ 6 = 2 (quotient), remainder = 12 − (6×2) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 12 and 30 is 6.
Common Mistakes and How to Avoid Them in GCF of 12 and 30
Finding GCF of 12 and 30 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 12, 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 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 odd number
Students may assume that the GCF of two numbers will always be an odd number. But it's not true; a GCF can also be an even number. To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 12 and 30 Examples
Problem 1
A teacher has 12 apples and 30 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 12 and 30 GCF of 12 and 30 2 × 3 = 6. There are 6 equal groups 12 ÷ 6 = 2 30 ÷ 6 = 5 There will be 6 groups, and each group gets 2 apples and 5 oranges.
Explanation
As the GCF of 12 and 30 is 6, the teacher can make 6 groups. Now divide 12 and 30 by 6. Each group gets 2 apples and 5 oranges.
Problem 2
A school has 12 red banners and 30 blue banners. They want to arrange them in rows with the same number of banners in each row, using the largest possible number of banners per row. How many banners will be in each row?
GCF of 12 and 30 2 × 3 = 6. So each row will have 6 banners.
Explanation
There are 12 red and 30 blue banners. To find the total number of banners in each row, we should find the GCF of 12 and 30. There will be 6 banners in each row.
Problem 3
A tailor has 12 meters of red fabric and 30 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 12 and 30 The GCF of 12 and 30 2 × 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 12 and 30, which is 6. The length of each piece of the fabric will be 6 meters.
Problem 4
A carpenter has two wooden planks, one 12 cm long and the other 30 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 12 and 30 2 × 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, 12 cm and 30 cm, respectively, we have to find the GCF of 12 and 30, which is 6 cm. The longest length of each piece is 6 cm.
Problem 5
If the GCF of 12 and ‘b’ is 6, and the LCM is 60, find ‘b’.
The value of ‘b’ is 30.
Explanation
GCF × LCM = product of the numbers 6 × 60 = 12 × b 360 = 12b b = 360 ÷ 12 = 30
FAQs on the Greatest Common Factor of 12 and 30
1.What is the LCM of 12 and 30?
2.Is 12 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 30?
5.Are 12 and 30 prime numbers?
Important Glossaries for GCF of 12 and 30
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- Prime Factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 30 is 2 × 3 × 5.
- Quotient: The result obtained by dividing one number by another. For example, when dividing 30 by 12, the quotient is 2.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 30 is divided by 12, the remainder is 6.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 12 and 30 is 60.
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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.
