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GCF of 27 and 36

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

1.	GCF of 27 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 27 and 36?

Answer: GCF of 27 and 36 is 9.

Explanation:

The GCF of two non-zero integers, x(27) and y(36), is the greatest positive integer m(9) that divides both x(27) and y(36) without any remainder.

Methods to Find GCF of 27 and 36

Let's look at the different methods for finding the GCF of 27 and 36.

Prime Factorization Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 27 and 36 by Prime Factorization

Prime factorization of 27 and 36 is (3 × 3 × 3) and (2 × 2 × 3 × 3) respectively. As visible, 27 and 36 have common prime factors. Hence, the GCF of 27 and 36 is 3 × 3 = 9.

GCF of 27 and 36 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 = 36 and Y = 27

GCF(36, 27) = GCF(27, 36 mod 27) = GCF(27, 9)
GCF(27, 9) = GCF(9, 27 mod 9) = GCF(9, 0)
GCF(9, 0) = 9 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 27 and 36 is 9.

GCF of 27 and 36 by Listing Common Factors

Factors of 27: 1, 3, 9, 27
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

There are 3 common factors of 27 and 36, that are 1, 3, and 9. Therefore, the greatest common factor of 27 and 36 is 9.

☛ Also Check:

GCF of 27 and 36 Examples

Example 1: Find the GCF of 27 and 36, if their LCM is 108.

Solution:

∵ LCM × GCF = 27 × 36
⇒ GCF(27, 36) = (27 × 36)/108 = 9
Therefore, the greatest common factor of 27 and 36 is 9.
Example 2: For two numbers, GCF = 9 and LCM = 108. If one number is 36, find the other number.

Solution:

Given: GCF (y, 36) = 9 and LCM (y, 36) = 108
∵ GCF × LCM = 36 × (y)
⇒ y = (GCF × LCM)/36
⇒ y = (9 × 108)/36
⇒ y = 27
Therefore, the other number is 27.
Example 3: The product of two numbers is 972. If their GCF is 9, what is their LCM?

Solution:

Given: GCF = 9 and product of numbers = 972
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 972/9
Therefore, the LCM is 108.

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FAQs on GCF of 27 and 36

What is the GCF of 27 and 36?

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

How to Find the GCF of 27 and 36 by Prime Factorization?

To find the GCF of 27 and 36, we will find the prime factorization of the given numbers, i.e. 27 = 3 × 3 × 3; 36 = 2 × 2 × 3 × 3.
⇒ Since 3, 3 are common terms in the prime factorization of 27 and 36. Hence, GCF(27, 36) = 3 × 3 = 9
☛ What is a Prime Number?

If the GCF of 36 and 27 is 9, Find its LCM.

GCF(36, 27) × LCM(36, 27) = 36 × 27
Since the GCF of 36 and 27 = 9
⇒ 9 × LCM(36, 27) = 972
Therefore, LCM = 108
☛ GCF Calculator

How to Find the GCF of 27 and 36 by Long Division Method?

To find the GCF of 27, 36 using long division method, 36 is divided by 27. The corresponding divisor (9) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 27 and 36?

There are three commonly used methods to find the GCF of 27 and 36.

By Long Division
By Prime Factorization
By Euclidean Algorithm

What is the Relation Between LCM and GCF of 27, 36?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 27 and 36, i.e. GCF × LCM = 27 × 36.

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