GCF of 18 and 81
2026-02-28 12:59 Diff
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Last updated on August 12, 2025

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 -

  1. Listing Factors
  2. Prime Factorization
  3. 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.

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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.

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?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 5

If the GCF of 18 and ‘b’ is 9, and the LCM is 162, find ‘b’.

Okay, lets begin

The value of ‘b’ is 81.

Explanation

GCF × LCM = product of the numbers

9 × 162 = 18 × b

1458 = 18b

b = 1458 ÷ 18 = 81

Well explained 👍

FAQs on the Greatest Common Factor of 18 and 81

1.What is the LCM of 18 and 81?

The LCM of 18 and 81 is 162.

2.Is 18 divisible by 2?

Yes, 18 is divisible by 2 because it is an even number.

3.What will be the GCF of any two prime numbers?

The common factor of prime numbers is 1 and the number itself. Since 1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.

4.What is the prime factorization of 81?

The prime factorization of 81 is 3⁴.

5.Are 18 and 81 prime numbers?

No, 18 and 81 are not prime numbers because both of them have more than two factors.

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.

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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.