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

GCF of 54 and 135

GCF of 54 and 135 is the largest possible number that divides 54 and 135 exactly without any remainder. The factors of 54 and 135 are 1, 2, 3, 6, 9, 18, 27, 54 and 1, 3, 5, 9, 15, 27, 45, 135 respectively. There are 3 commonly used methods to find the GCF of 54 and 135 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 54 and 135
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 54 and 135?

Answer: GCF of 54 and 135 is 27.

Explanation:

The GCF of two non-zero integers, x(54) and y(135), is the greatest positive integer m(27) that divides both x(54) and y(135) without any remainder.

Methods to Find GCF of 54 and 135

The methods to find the GCF of 54 and 135 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 54 and 135 by Long Division

GCF of 54 and 135 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 135 (larger number) by 54 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (54) by the remainder (27).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (27) is the GCF of 54 and 135.

GCF of 54 and 135 by Prime Factorization

Prime factorization of 54 and 135 is (2 × 3 × 3 × 3) and (3 × 3 × 3 × 5) respectively. As visible, 54 and 135 have common prime factors. Hence, the GCF of 54 and 135 is 3 × 3 × 3 = 27.

GCF of 54 and 135 by Listing Common Factors

Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135

There are 4 common factors of 54 and 135, that are 27, 1, 3, and 9. Therefore, the greatest common factor of 54 and 135 is 27.

☛ Also Check:

GCF of 54 and 135 Examples

Example 1: Find the GCF of 54 and 135, if their LCM is 270.

Solution:

∵ LCM × GCF = 54 × 135
⇒ GCF(54, 135) = (54 × 135)/270 = 27
Therefore, the greatest common factor of 54 and 135 is 27.
Example 2: Find the greatest number that divides 54 and 135 exactly.

Solution:

The greatest number that divides 54 and 135 exactly is their greatest common factor, i.e. GCF of 54 and 135.
⇒ Factors of 54 and 135:
- Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54
- Factors of 135 = 1, 3, 5, 9, 15, 27, 45, 135
Therefore, the GCF of 54 and 135 is 27.
Example 3: For two numbers, GCF = 27 and LCM = 270. If one number is 135, find the other number.

Solution:

Given: GCF (y, 135) = 27 and LCM (y, 135) = 270
∵ GCF × LCM = 135 × (y)
⇒ y = (GCF × LCM)/135
⇒ y = (27 × 270)/135
⇒ y = 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 135

What is the GCF of 54 and 135?

The GCF of 54 and 135 is 27. To calculate the greatest common factor of 54 and 135, we need to factor each number (factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54; factors of 135 = 1, 3, 5, 9, 15, 27, 45, 135) and choose the greatest factor that exactly divides both 54 and 135, i.e., 27.

If the GCF of 135 and 54 is 27, Find its LCM.

GCF(135, 54) × LCM(135, 54) = 135 × 54
Since the GCF of 135 and 54 = 27
⇒ 27 × LCM(135, 54) = 7290
Therefore, LCM = 270
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 54 and 135?

There are three commonly used methods to find the GCF of 54 and 135.

By Listing Common Factors
By Prime Factorization
By Long Division

How to Find the GCF of 54 and 135 by Prime Factorization?

To find the GCF of 54 and 135, we will find the prime factorization of the given numbers, i.e. 54 = 2 × 3 × 3 × 3; 135 = 3 × 3 × 3 × 5.
⇒ Since 3, 3, 3 are common terms in the prime factorization of 54 and 135. Hence, GCF(54, 135) = 3 × 3 × 3 = 27
☛ What are Prime Numbers?

What is the Relation Between LCM and GCF of 54, 135?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 54 and 135, i.e. GCF × LCM = 54 × 135.

How to Find the GCF of 54 and 135 by Long Division Method?

To find the GCF of 54, 135 using long division method, 135 is divided by 54. The corresponding divisor (27) when remainder equals 0 is taken as GCF.

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum