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105 LearnersLast updated on September 24, 2025
GCF of 6 and 20
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 6 and 20.
What is the GCF of 6 and 20?
The greatest common factor of 6 and 20 is 2. 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 6 and 20?
To find the GCF of 6 and 20, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 6 and 20 by Using Listing of Factors
Steps to find the GCF of 6 and 20 using the listing of factors:
Step 1: Firstly, list the factors of each number. Factors of 6 = 1, 2, 3, 6. Factors of 20 = 1, 2, 4, 5, 10, 20.
Step 2: Now, identify the common factors of them. Common factor of 6 and 20: 1, 2.
Step 3: Choose the largest factor. The largest factor that both numbers have is 2. The GCF of 6 and 20 is 2.
GCF of 6 and 20 Using Prime Factorization
To find the GCF of 6 and 20 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number. Prime Factors of 6: 6 = 2 x 3 Prime Factors of 20: 20 = 2 x 2 x 5
Step 2: Now, identify the common prime factors. The common prime factor is: 2
Step 3: Multiply the common prime factors. The Greatest Common Factor of 6 and 20 is 2.
GCF of 6 and 20 Using Division Method or Euclidean Algorithm Method
Find the GCF of 6 and 20 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number. Here, divide 20 by 6. 20 ÷ 6 = 3 (quotient), The remainder is calculated as 20 − (6×3) = 2. The remainder is 2, not zero, so continue the process.
Step 2: Now divide the previous divisor (6) by the previous remainder (2). Divide 6 by 2. 6 ÷ 2 = 3 (quotient), remainder = 6 − (2×3) = 0. The remainder is zero, the divisor will become the GCF. The GCF of 6 and 20 is 2.
Common Mistakes and How to Avoid Them in GCF of 6 and 20
Finding GCF of 6 and 20 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 20, students may mention 3, 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 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 6 and 20 Examples
Problem 1
A baker has 6 chocolate bars and 20 candies. She wants to package them into equal sets, with the largest number of items in each set. How many items will be in each set?
We should find the GCF of 6 and 20. GCF of 6 and 20 is 2. There are 2 equal groups. 6 ÷ 2 = 3 20 ÷ 2 = 10 There will be 2 groups, and each group gets 3 chocolate bars and 10 candies.
Explanation
As the GCF of 6 and 20 is 2, the baker can make 2 groups.
Now divide 6 and 20 by 2.
Each group gets 3 chocolate bars and 10 candies.
Problem 2
A gardener has 6 rose bushes and 20 tulip plants. They want to arrange them in rows with the same number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?
GCF of 6 and 20 is 2. So each row will have 2 plants.
Explanation
There are 6 rose bushes and 20 tulip plants.
To find the total number of plants in each row, we should find the GCF of 6 and 20.
There will be 2 plants in each row.
Problem 3
A seamstress has 6 meters of blue fabric and 20 meters of red 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 6 and 20. The GCF of 6 and 20 is 2. The fabric is 2 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 6 and 20, which is 2.
The length of each piece of fabric will be 2 meters.
Problem 4
A carpenter has two wooden planks, one 6 cm long and the other 20 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 6 and 20 is 2. The longest length of each piece is 2 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 6 cm and 20 cm, respectively, we have to find the GCF of 6 and 20, which is 2 cm.
The longest length of each piece is 2 cm.
Problem 5
If the GCF of 6 and ‘b’ is 2, and the LCM is 30, find ‘b’.
The value of ‘b’ is 10.
Explanation
GCF x LCM = product of the numbers
2 × 30 = 6 × b
60 = 6b
b = 60 ÷ 6
= 10
FAQs on the Greatest Common Factor of 6 and 20
1.What is the LCM of 6 and 20?
2.Is 6 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 20?
5.Are 6 and 20 prime numbers?
Important Glossaries for GCF of 6 and 20
- 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, 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 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.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 6 and 20 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.
