A day full of math games & activities. Find one near you.

GCF of 54 and 27

GCF of 54 and 27 is the largest possible number that divides 54 and 27 exactly without any remainder. The factors of 54 and 27 are 1, 2, 3, 6, 9, 18, 27, 54 and 1, 3, 9, 27 respectively. There are 3 commonly used methods to find the GCF of 54 and 27 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 54 and 27
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 54 and 27?

Answer: GCF of 54 and 27 is 27.

Explanation:

The GCF of two non-zero integers, x(54) and y(27), is the greatest positive integer m(27) that divides both x(54) and y(27) without any remainder.

Methods to Find GCF of 54 and 27

The methods to find the GCF of 54 and 27 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 54 and 27 by Long Division

GCF of 54 and 27 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 54 (larger number) by 27 (smaller number).
Step 2: Since the remainder = 0, the divisor (27) is the GCF of 54 and 27.

The corresponding divisor (27) is the GCF of 54 and 27.

GCF of 54 and 27 by Prime Factorization

Prime factorization of 54 and 27 is (2 × 3 × 3 × 3) and (3 × 3 × 3) respectively. As visible, 54 and 27 have common prime factors. Hence, the GCF of 54 and 27 is 3 × 3 × 3 = 27.

GCF of 54 and 27 by Listing Common Factors

Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
Factors of 27: 1, 3, 9, 27

There are 4 common factors of 54 and 27, that are 3, 1, 27, and 9. Therefore, the greatest common factor of 54 and 27 is 27.

☛ Also Check:

GCF of 54 and 27 Examples

Example 1: Find the GCF of 54 and 27, if their LCM is 54.

Solution:

∵ LCM × GCF = 54 × 27
⇒ GCF(54, 27) = (54 × 27)/54 = 27
Therefore, the greatest common factor of 54 and 27 is 27.
Example 2: The product of two numbers is 1458. If their GCF is 27, what is their LCM?

Solution:

Given: GCF = 27 and product of numbers = 1458
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1458/27
Therefore, the LCM is 54.
Example 3: For two numbers, GCF = 27 and LCM = 54. If one number is 27, find the other number.

Solution:

Given: GCF (x, 27) = 27 and LCM (x, 27) = 54
∵ GCF × LCM = 27 × (x)
⇒ x = (GCF × LCM)/27
⇒ x = (27 × 54)/27
⇒ x = 54
Therefore, the other number is 54.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on GCF of 54 and 27

What is the GCF of 54 and 27?

The GCF of 54 and 27 is 27. To calculate the GCF (Greatest Common Factor) of 54 and 27, we need to factor each number (factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54; factors of 27 = 1, 3, 9, 27) and choose the greatest factor that exactly divides both 54 and 27, i.e., 27.

How to Find the GCF of 54 and 27 by Prime Factorization?

To find the GCF of 54 and 27, we will find the prime factorization of the given numbers, i.e. 54 = 2 × 3 × 3 × 3; 27 = 3 × 3 × 3.
⇒ Since 3, 3, 3 are common terms in the prime factorization of 54 and 27. Hence, GCF(54, 27) = 3 × 3 × 3 = 27
☛ Prime Numbers

If the GCF of 27 and 54 is 27, Find its LCM.

GCF(27, 54) × LCM(27, 54) = 27 × 54
Since the GCF of 27 and 54 = 27
⇒ 27 × LCM(27, 54) = 1458
Therefore, LCM = 54
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 54, 27?

The following equation can be used to express the relation between LCM and GCF of 54 and 27, i.e. GCF × LCM = 54 × 27.

What are the Methods to Find GCF of 54 and 27?

There are three commonly used methods to find the GCF of 54 and 27.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 54 and 27 by Long Division Method?

To find the GCF of 54, 27 using long division method, 54 is divided by 27. The corresponding divisor (27) when remainder equals 0 is taken as GCF.

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum