100 LearnersLast updated on August 12th, 2025
GCF of 18 and 81
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 81.
What is the GCF of 18 and 81?
The greatest common factor of 18 and 81 is 9. 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 81?
To find the GCF of 18 and 81, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 18 and 81 by Using Listing of Factors
Steps to find the GCF of 18 and 81 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 81 = 1, 3, 9, 27, 81.
Step 2: Now, identify the common factors of them Common factors of 18 and 81: 1, 3, 9.
Step 3: Choose the largest factor The largest factor that both numbers have is 9. The GCF of 18 and 81 is 9.
GCF of 18 and 81 Using Prime Factorization
To find the GCF of 18 and 81 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 81: 81 = 3 × 3 × 3 × 3 = 3⁴
Step 2: Now, identify the common prime factors The common prime factors are: 3 × 3 = 3²
Step 3: Multiply the common prime factors 3² = 9. The Greatest Common Factor of 18 and 81 is 9.
GCF of 18 and 81 Using Division Method or Euclidean Algorithm Method
Find the GCF of 18 and 81 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 81 by 18 81 ÷ 18 = 4 (quotient), The remainder is calculated as 81 − (18×4) = 9 The remainder is 9, not zero, so continue the process
Step 2: Now divide the previous divisor (18) by the previous remainder (9) Divide 18 by 9 18 ÷ 9 = 2 (quotient), remainder = 18 − (9×2) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 18 and 81 is 9.
Common Mistakes and How to Avoid Them in GCF of 18 and 81
Finding GCF of 18 and 81 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 10 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 tells about the 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 18 and 81 Examples
Problem 1
A librarian has 18 fiction books and 81 non-fiction books. She wants to organize them into equal groups, with the largest number of books in each group. How many books will be in each group?
We should find the GCF of 18 and 81 GCF of 18 and 81 3² = 9.
There are 9 equal groups 18 ÷ 9 = 2 81 ÷ 9 = 9 There will be 9 groups, and each group gets 2 fiction books and 9 non-fiction books.
Explanation
As the GCF of 18 and 81 is 9, the librarian can make 9 groups. Now divide 18 and 81 by 9. Each group gets 2 fiction books and 9 non-fiction books.
Problem 2
A band has 18 guitars and 81 drums. They want to arrange them in rows with the same number of instruments in each row, using the largest possible number of instruments per row. How many instruments will be in each row?
GCF of 18 and 81 3² = 9. So each row will have 9 instruments.
Explanation
There are 18 guitars and 81 drums. To find the total number of instruments in each row, we should find the GCF of 18 and 81. There will be 9 instruments in each row.
Problem 3
A chef has 18 kilograms of flour and 81 kilograms of sugar. She wants to package them into bags of equal weight, using the largest possible weight. What should be the weight of each bag?
For calculating the longest equal weight, we have to calculate the GCF of 18 and 81 The GCF of 18 and 81 3² = 9. Each bag will weigh 9 kilograms.
Explanation
For calculating the longest weight for packaging, first we need to calculate the GCF of 18 and 81 which is 9. The weight of each bag will be 9 kilograms.
Problem 4
A construction company has two cables, one 18 meters long and the other 81 meters long. They want to cut them into the longest possible equal pieces, without any cable left over. What should be the length of each piece?
The construction company needs the longest piece of cable GCF of 18 and 81 3² = 9. The longest length of each piece is 9 meters.
Explanation
To find the longest length of each piece of the two cables, 18 meters and 81 meters, respectively. We have to find the GCF of 18 and 81, which is 9 meters. The longest length of each piece is 9 meters.
Problem 5
If the GCF of 18 and ‘b’ is 9, and the LCM is 162, find ‘b’.
The value of ‘b’ is 81.
Explanation
GCF × LCM = product of the numbers
9 × 162 = 18 × b
1458 = 18b
b = 1458 ÷ 18 = 81
FAQs on the Greatest Common Factor of 18 and 81
1.What is the LCM of 18 and 81?
2.Is 18 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 81?
5.Are 18 and 81 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 18 and 81?
7.What are some fun ways kids in United States can practice GCF of 18 and 81 with numbers?
8.What role do numbers and GCF of 18 and 81 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve GCF of 18 and 81 skills?
Important Glossaries for GCF of 18 and 81
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.
- 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 18 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 19 is divided by 5, the remainder is 4 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 81 is 162.
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.
