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GCF of 81 and 108

GCF of 81 and 108 is the largest possible number that divides 81 and 108 exactly without any remainder. The factors of 81 and 108 are 1, 3, 9, 27, 81 and 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 respectively. There are 3 commonly used methods to find the GCF of 81 and 108 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 81 and 108
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 81 and 108?

Answer: GCF of 81 and 108 is 27.

Explanation:

The GCF of two non-zero integers, x(81) and y(108), is the greatest positive integer m(27) that divides both x(81) and y(108) without any remainder.

Methods to Find GCF of 81 and 108

The methods to find the GCF of 81 and 108 are explained below.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

GCF of 81 and 108 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 = 108 and Y = 81

GCF(108, 81) = GCF(81, 108 mod 81) = GCF(81, 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 81 and 108 is 27.

GCF of 81 and 108 by Prime Factorization

Prime factorization of 81 and 108 is (3 × 3 × 3 × 3) and (2 × 2 × 3 × 3 × 3) respectively. As visible, 81 and 108 have common prime factors. Hence, the GCF of 81 and 108 is 3 × 3 × 3 = 27.

GCF of 81 and 108 by Long Division

GCF of 81 and 108 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 108 (larger number) by 81 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (81) by the remainder (27).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (27) is the GCF of 81 and 108.

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GCF of 81 and 108 Examples

Example 1: The product of two numbers is 8748. If their GCF is 27, what is their LCM?

Solution:

Given: GCF = 27 and product of numbers = 8748
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 8748/27
Therefore, the LCM is 324.
Example 2: Find the GCF of 81 and 108, if their LCM is 324.

Solution:

∵ LCM × GCF = 81 × 108
⇒ GCF(81, 108) = (81 × 108)/324 = 27
Therefore, the greatest common factor of 81 and 108 is 27.
Example 3: For two numbers, GCF = 27 and LCM = 324. If one number is 108, find the other number.

Solution:

Given: GCF (z, 108) = 27 and LCM (z, 108) = 324
∵ GCF × LCM = 108 × (z)
⇒ z = (GCF × LCM)/108
⇒ z = (27 × 324)/108
⇒ z = 81
Therefore, the other number is 81.

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FAQs on GCF of 81 and 108

What is the GCF of 81 and 108?

The GCF of 81 and 108 is 27. To calculate the GCF (Greatest Common Factor) of 81 and 108, we need to factor each number (factors of 81 = 1, 3, 9, 27, 81; factors of 108 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108) and choose the greatest factor that exactly divides both 81 and 108, i.e., 27.

What are the Methods to Find GCF of 81 and 108?

There are three commonly used methods to find the GCF of 81 and 108.

By Long Division
By Listing Common Factors
By Prime Factorization

If the GCF of 108 and 81 is 27, Find its LCM.

GCF(108, 81) × LCM(108, 81) = 108 × 81
Since the GCF of 108 and 81 = 27
⇒ 27 × LCM(108, 81) = 8748
Therefore, LCM = 324
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How to Find the GCF of 81 and 108 by Long Division Method?

To find the GCF of 81, 108 using long division method, 108 is divided by 81. The corresponding divisor (27) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 81, 108?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 81 and 108, i.e. GCF × LCM = 81 × 108.

How to Find the GCF of 81 and 108 by Prime Factorization?

To find the GCF of 81 and 108, we will find the prime factorization of the given numbers, i.e. 81 = 3 × 3 × 3 × 3; 108 = 2 × 2 × 3 × 3 × 3.
⇒ Since 3, 3, 3 are common terms in the prime factorization of 81 and 108. Hence, GCF(81, 108) = 3 × 3 × 3 = 27
☛ What is a Prime Number?

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