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GCF of 27 and 81

GCF of 27 and 81 is the largest possible number that divides 27 and 81 exactly without any remainder. The factors of 27 and 81 are 1, 3, 9, 27 and 1, 3, 9, 27, 81 respectively. There are 3 commonly used methods to find the GCF of 27 and 81 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 27 and 81
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 27 and 81?

Answer: GCF of 27 and 81 is 27.

Explanation:

The GCF of two non-zero integers, x(27) and y(81), is the greatest positive integer m(27) that divides both x(27) and y(81) without any remainder.

Methods to Find GCF of 27 and 81

Let's look at the different methods for finding the GCF of 27 and 81.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 27 and 81 by Long Division

GCF of 27 and 81 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 81 (larger number) by 27 (smaller number).
Step 2: Since the remainder = 0, the divisor (27) is the GCF of 27 and 81.

The corresponding divisor (27) is the GCF of 27 and 81.

GCF of 27 and 81 by Listing Common Factors

Factors of 27: 1, 3, 9, 27
Factors of 81: 1, 3, 9, 27, 81

There are 4 common factors of 27 and 81, that are 3, 1, 27, and 9. Therefore, the greatest common factor of 27 and 81 is 27.

GCF of 27 and 81 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 = 81 and Y = 27

GCF(81, 27) = GCF(27, 81 mod 27) = GCF(27, 0)
GCF(27, 0) = 27 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 27 and 81 is 27.

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GCF of 27 and 81 Examples

Example 1: The product of two numbers is 2187. If their GCF is 27, what is their LCM?

Solution:

Given: GCF = 27 and product of numbers = 2187
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2187/27
Therefore, the LCM is 81.
Example 2: Find the greatest number that divides 27 and 81 exactly.

Solution:

The greatest number that divides 27 and 81 exactly is their greatest common factor, i.e. GCF of 27 and 81.
⇒ Factors of 27 and 81:
- Factors of 27 = 1, 3, 9, 27
- Factors of 81 = 1, 3, 9, 27, 81
Therefore, the GCF of 27 and 81 is 27.
Example 3: Find the GCF of 27 and 81, if their LCM is 81.

Solution:

∵ LCM × GCF = 27 × 81
⇒ GCF(27, 81) = (27 × 81)/81 = 27
Therefore, the greatest common factor of 27 and 81 is 27.

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FAQs on GCF of 27 and 81

What is the GCF of 27 and 81?

The GCF of 27 and 81 is 27. To calculate the GCF (Greatest Common Factor) of 27 and 81, we need to factor each number (factors of 27 = 1, 3, 9, 27; factors of 81 = 1, 3, 9, 27, 81) and choose the greatest factor that exactly divides both 27 and 81, i.e., 27.

What are the Methods to Find GCF of 27 and 81?

There are three commonly used methods to find the GCF of 27 and 81.

By Prime Factorization
By Long Division
By Listing Common Factors

If the GCF of 81 and 27 is 27, Find its LCM.

GCF(81, 27) × LCM(81, 27) = 81 × 27
Since the GCF of 81 and 27 = 27
⇒ 27 × LCM(81, 27) = 2187
Therefore, LCM = 81
☛ Greatest Common Factor Calculator

How to Find the GCF of 27 and 81 by Long Division Method?

To find the GCF of 27, 81 using long division method, 81 is divided by 27. The corresponding divisor (27) when remainder equals 0 is taken as GCF.

How to Find the GCF of 27 and 81 by Prime Factorization?

To find the GCF of 27 and 81, we will find the prime factorization of the given numbers, i.e. 27 = 3 × 3 × 3; 81 = 3 × 3 × 3 × 3.
⇒ Since 3, 3, 3 are common terms in the prime factorization of 27 and 81. Hence, GCF(27, 81) = 3 × 3 × 3 = 27
☛ Prime Number

What is the Relation Between LCM and GCF of 27, 81?

The following equation can be used to express the relation between LCM and GCF of 27 and 81, i.e. GCF × LCM = 27 × 81.

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