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103 LearnersLast updated on September 25, 2025
GCF of 18 and 66
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 18 and 66.
What is the GCF of 18 and 66?
The greatest common factor of 18 and 66 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 18 and 66?
To find the GCF of 18 and 66, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 18 and 66 by Using Listing of Factors
Steps to find the GCF of 18 and 66 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 18 = 1, 2, 3, 6, 9, 18. Factors of 66 = 1, 2, 3, 6, 11, 22, 33, 66.
Step 2: Now, identify the common factors of them Common factors of 18 and 66: 1, 2, 3, 6.
Step 3: Choose the largest factor The largest factor that both numbers have is 6. The GCF of 18 and 66 is 6.
GCF of 18 and 66 Using Prime Factorization
To find the GCF of 18 and 66 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 18: 18 = 2 × 3 × 3 = 2 × 3² Prime Factors of 66: 66 = 2 × 3 × 11
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 18 and 66 is 6.
GCF of 18 and 66 Using Division Method or Euclidean Algorithm Method
Find the GCF of 18 and 66 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 66 by 18 66 ÷ 18 = 3 (quotient), The remainder is calculated as 66 − (18×3) = 12 The remainder is 12, not zero, so continue the process
Step 2: Now divide the previous divisor (18) by the previous remainder (12) Divide 18 by 12 18 ÷ 12 = 1 (quotient), remainder = 18 − (12×1) = 6 The remainder is 6, not zero, so continue the process
Step 3: Now divide the previous divisor (12) by the remainder (6) 12 ÷ 6 = 2 (quotient), remainder = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 18 and 66 is 6.
Common Mistakes and How to Avoid Them in GCF of 18 and 66
Finding GCF of 18 and 66 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 18, 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 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 18 and 66 Examples
Problem 1
A chef has 18 apples and 66 oranges. He wants to make fruit baskets with the largest equal number of fruits in each basket. How many fruits will be in each basket?
We should find the GCF of 18 and 66. GCF of 18 and 66 2 × 3 = 6. There are 6 equal groups. 18 ÷ 6 = 3 66 ÷ 6 = 11 There will be 6 baskets, and each basket gets 3 apples and 11 oranges.
Explanation
As the GCF of 18 and 66 is 6, the chef can make 6 baskets.
Now divide 18 and 66 by 6.
Each basket gets 3 apples and 11 oranges.
Problem 2
A gardener has 18 red roses and 66 white roses. They want to arrange them in vases with the same number of roses in each vase, using the largest possible number of roses per vase. How many roses will be in each vase?
GCF of 18 and 66 2 × 3 = 6. So each vase will have 6 roses.
Explanation
There are 18 red roses and 66 white roses.
To find the total number of roses in each vase, we should find the GCF of 18 and 66.
There will be 6 roses in each vase.
Problem 3
A tailor has 18 meters of silk ribbon and 66 meters of cotton 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 18 and 66. The GCF of 18 and 66 2 × 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 18 and 66, which is 6.
The length of each piece of the ribbon will be 6 meters.
Problem 4
A carpenter has two wooden planks, one 18 cm long and the other 66 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 18 and 66 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, 18 cm and 66 cm, respectively.
We have to find the GCF of 18 and 66, which is 6 cm.
The longest length of each piece is 6 cm.
Problem 5
If the GCF of 18 and ‘a’ is 6, and the LCM is 198. Find ‘a’.
The value of ‘a’ is 66.
Explanation
GCF × LCM = product of the numbers
6 × 198 = 18 × a
1188 = 18a
a = 1188 ÷ 18
= 66
FAQs on the Greatest Common Factor of 18 and 66
1.What is the LCM of 18 and 66?
2.Is 18 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 66?
5.Are 18 and 66 prime numbers?
Important Glossaries for GCF of 18 and 66
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 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 18 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 4, the remainder is 1 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 18 and 66 is 198.
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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.
