GCF of 18 and 27
2026-02-28 13:15 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 items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 18 and 27.

What is the GCF of 18 and 27?

The greatest common factor of 18 and 27 is 9. The largest divisor of two or more numbers is called the GCF of the numbers.

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 27?

To find the GCF of 18 and 27, a few methods are described below - Listing Factors Prime Factorization Long Division Method / Euclidean Algorithm

GCF of 18 and 27 by Using Listing of Factors

Steps to find the GCF of 18 and 27 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 27 = 1, 3, 9, 27.

Step 2: Now, identify the common factors of them Common factors of 18 and 27: 1, 3, 9.

Step 3: Choose the largest factor The largest factor that both numbers have is 9.

The GCF of 18 and 27 is 9.

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GCF of 18 and 27 Using Prime Factorization

To find the GCF of 18 and 27 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 27: 27 = 3 × 3 × 3 = 3³

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 27 is 9.

GCF of 18 and 27 Using Division Method or Euclidean Algorithm Method

Find the GCF of 18 and 27 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number Here, divide 27 by 18 27 ÷ 18 = 1 (quotient), The remainder is calculated as 27 − (18×1) = 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 27 is 9.

Common Mistakes and How to Avoid Them in GCF of 18 and 27

Finding the GCF of 18 and 27 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 chef has 18 apples and 27 oranges. She wants to create fruit baskets with the largest number of equal pieces of fruit. How many pieces of fruit will be in each basket?

Okay, lets begin

We should find the GCF of 18 and 27 GCF of 18 and 27 3² = 9.

There are 9 equal groups 18 ÷ 9 = 2 27 ÷ 9 = 3

There will be 9 baskets, and each basket gets 2 apples and 3 oranges.

Explanation

As the GCF of 18 and 27 is 9, the chef can make 9 baskets. Now divide 18 and 27 by 9. Each basket gets 2 apples and 3 oranges.

Well explained 👍

Problem 2

A classroom has 18 desks and 27 chairs. They want to arrange them in rows with the same number of desks and chairs in each row, using the largest possible number of items per row. How many items will be in each row?

Okay, lets begin

GCF of 18 and 27 3² = 9. So each row will have 9 items.

Explanation

There are 18 desks and 27 chairs. To find the total number of items in each row, we should find the GCF of 18 and 27. There will be 9 items in each row.

Well explained 👍

Problem 3

A landscaper has 18 meters of red fencing and 27 meters of blue fencing. She wants to cut both fences into pieces of equal length, using the longest possible length. What should be the length of each piece?

Okay, lets begin

For calculating the longest equal length, we have to calculate the GCF of 18 and 27

The GCF of 18 and 27 3² = 9. The fencing is 9 meters long.

Explanation

For calculating the longest length of the fencing, first we need to calculate the GCF of 18 and 27, which is 9. The length of each piece of fencing will be 9 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 18 cm long and the other 27 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?

Okay, lets begin

The carpenter needs the longest piece of wood GCF of 18 and 27 3² = 9. The longest length of each piece is 9 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 18 cm and 27 cm respectively, we have to find the GCF of 18 and 27, which is 9 cm. The longest length of each piece is 9 cm.

Well explained 👍

Problem 5

If the GCF of 18 and ‘b’ is 9, and the LCM is 54. Find ‘b’.

Okay, lets begin

The value of ‘b’ is 27.

Explanation

GCF x LCM = product of the numbers

9 × 54 = 18 × b

486 = 18b b = 486 ÷ 18 = 27

Well explained 👍

FAQs on the Greatest Common Factor of 18 and 27

1.What is the LCM of 18 and 27?

The LCM of 18 and 27 is 54.

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 27?

The prime factorization of 27 is 3³.

5.Are 18 and 27 prime numbers?

No, 18 and 27 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 18 and 27

  • 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, 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 18 are 2 and 3.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 28 is divided by 5, the remainder is 3 and the quotient is 5.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 18 and 27 is 54.

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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.