106 LearnersLast updated on August 5th, 2025
GCF of 6 and 18
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 6 and 18.
What is the GCF of 6 and 18?
The greatest common factor of 6 and 18 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 6 and 18?
To find the GCF of 6 and 18, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 6 and 18 by Using Listing of factors
Steps to find the GCF of 6 and 18 using the listing of factors:
Step 1: First, list the factors of each number
Factors of 6 = 1, 2, 3, 6.
Factors of 18 = 1, 2, 3, 6, 9, 18.
Step 2: Now, identify the common factors of them Common factors of 6 and 18: 1, 2, 3, 6.
Step 3: Choose the largest factor The largest factor that both numbers have is 6.
The GCF of 6 and 18 is 6.
GCF of 6 and 18 Using Prime Factorization
To find the GCF of 6 and 18 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 6: 6 = 2 × 3
Prime Factors of 18: 18 = 2 × 3 × 3
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 6 and 18 is 6.
GCF of 6 and 18 Using Division Method or Euclidean Algorithm Method
Find the GCF of 6 and 18 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number.
Here, divide 18 by 6 18 ÷ 6 = 3 (quotient), remainder = 18 − (6×3) = 0
Step 2: Since the remainder is zero, the divisor will become the GCF.
The GCF of 6 and 18 is 6.
Common Mistakes and How to Avoid Them in GCF of 6 and 18
Finding GCF of 6 and 18 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 6, students may mention 4, 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 even number
Students may assume that the 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 6 and 18 Examples
Problem 1
A chef has 6 kilograms of flour and 18 kilograms of sugar. He wants to divide them into equal portions with the largest possible number of grams in each portion. How many grams will be in each portion?
We should find the GCF of 6 and 18 GCF of 6 and 18 is 6.
There are 6 equal portions
6 kg ÷ 6 = 1 kg
18 kg ÷ 6 = 3 kg
Each portion will have 1 kilogram of flour and 3 kilograms of sugar.
Explanation
As the GCF of 6 and 18 is 6, the chef can make 6 portions.
Now divide 6 and 18 by 6.
Each portion gets 1 kilogram of flour and 3 kilograms of sugar.
Problem 2
A gardener has 6 rose bushes and 18 tulip bulbs. She wants to plant 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 18 is 6. So each row will have 6 plants.
Explanation
There are 6 rose bushes and 18 tulip bulbs.
To find the total number of plants in each row, we should find the GCF of 6 and 18.
There will be 6 plants in each row.
Problem 3
A tailor has 6 meters of red fabric and 18 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 6 and 18.
The GCF of 6 and 18 is 6.
The fabric is 6 meters long.
Explanation
For calculating the longest length of the fabric, we first need to calculate the GCF of 6 and 18, which is 6.
The length of each piece of the fabric will be 6 meters.
Problem 4
A carpenter has two wooden planks, one 6 cm long and the other 18 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 18 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, 6 cm and 18 cm respectively, we have to find the GCF of 6 and 18, which is 6 cm. The longest length of each piece is 6 cm.
Problem 5
If the GCF of 6 and ‘b’ is 6, and the LCM is 18, find ‘b’.
The value of ‘b’ is 18.
Explanation
GCF × LCM = product of the numbers
6 × 18 = 6 × b
108 = 6b
b = 108 ÷ 6 = 18
FAQs on the Greatest Common Factor of 6 and 18
1.What is the LCM of 6 and 18?
2.Is 6 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 18?
5.Are 6 and 18 prime numbers?
6.How can children in Vietnam use numbers in everyday life to understand GCF of 6 and 18?
7.What are some fun ways kids in Vietnam can practice GCF of 6 and 18 with numbers?
8.What role do numbers and GCF of 6 and 18 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve GCF of 6 and 18 skills?
Important Glossaries for GCF of 6 and 18
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 20, 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 12 is divided by 7, the remainder is 5 and the quotient is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 6 and 18 is 18.
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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.
