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

GCF of 27 and 30

GCF of 27 and 30 is the largest possible number that divides 27 and 30 exactly without any remainder. The factors of 27 and 30 are 1, 3, 9, 27 and 1, 2, 3, 5, 6, 10, 15, 30 respectively. There are 3 commonly used methods to find the GCF of 27 and 30 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 27 and 30
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 27 and 30?

Answer: GCF of 27 and 30 is 3.

Explanation:

The GCF of two non-zero integers, x(27) and y(30), is the greatest positive integer m(3) that divides both x(27) and y(30) without any remainder.

Methods to Find GCF of 27 and 30

The methods to find the GCF of 27 and 30 are explained below.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 27 and 30 by Long Division

GCF of 27 and 30 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 30 (larger number) by 27 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (27) by the remainder (3).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 27 and 30.

GCF of 27 and 30 by Listing Common Factors

Factors of 27: 1, 3, 9, 27
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

There are 2 common factors of 27 and 30, that are 1 and 3. Therefore, the greatest common factor of 27 and 30 is 3.

GCF of 27 and 30 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 30 and Y = 27

GCF(30, 27) = GCF(27, 30 mod 27) = GCF(27, 3)
GCF(27, 3) = GCF(3, 27 mod 3) = GCF(3, 0)
GCF(3, 0) = 3 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 27 and 30 is 3.

☛ Also Check:

GCF of 27 and 30 Examples

Example 1: The product of two numbers is 810. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 810
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 810/3
Therefore, the LCM is 270.
Example 2: Find the greatest number that divides 27 and 30 exactly.

Solution:

The greatest number that divides 27 and 30 exactly is their greatest common factor, i.e. GCF of 27 and 30.
⇒ Factors of 27 and 30:
- Factors of 27 = 1, 3, 9, 27
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Therefore, the GCF of 27 and 30 is 3.
Example 3: For two numbers, GCF = 3 and LCM = 270. If one number is 27, find the other number.

Solution:

Given: GCF (y, 27) = 3 and LCM (y, 27) = 270
∵ GCF × LCM = 27 × (y)
⇒ y = (GCF × LCM)/27
⇒ y = (3 × 270)/27
⇒ y = 30
Therefore, the other number is 30.

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 27 and 30

What is the GCF of 27 and 30?

The GCF of 27 and 30 is 3. To calculate the greatest common factor (GCF) of 27 and 30, we need to factor each number (factors of 27 = 1, 3, 9, 27; factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30) and choose the greatest factor that exactly divides both 27 and 30, i.e., 3.

How to Find the GCF of 27 and 30 by Long Division Method?

To find the GCF of 27, 30 using long division method, 30 is divided by 27. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 27, 30?

The following equation can be used to express the relation between LCM and GCF of 27 and 30, i.e. GCF × LCM = 27 × 30.

How to Find the GCF of 27 and 30 by Prime Factorization?

To find the GCF of 27 and 30, we will find the prime factorization of the given numbers, i.e. 27 = 3 × 3 × 3; 30 = 2 × 3 × 5.
⇒ Since 3 is the only common prime factor of 27 and 30. Hence, GCF (27, 30) = 3.
☛ What is a Prime Number?

If the GCF of 30 and 27 is 3, Find its LCM.

GCF(30, 27) × LCM(30, 27) = 30 × 27
Since the GCF of 30 and 27 = 3
⇒ 3 × LCM(30, 27) = 810
Therefore, LCM = 270
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 27 and 30?

There are three commonly used methods to find the GCF of 27 and 30.

By Long Division
By Prime Factorization
By Listing Common Factors

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum