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GCF of 20 and 27

GCF of 20 and 27 is the largest possible number that divides 20 and 27 exactly without any remainder. The factors of 20 and 27 are 1, 2, 4, 5, 10, 20 and 1, 3, 9, 27 respectively. There are 3 commonly used methods to find the GCF of 20 and 27 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 20 and 27
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 20 and 27?

Answer: GCF of 20 and 27 is 1.

Explanation:

The GCF of two non-zero integers, x(20) and y(27), is the greatest positive integer m(1) that divides both x(20) and y(27) without any remainder.

Methods to Find GCF of 20 and 27

Let's look at the different methods for finding the GCF of 20 and 27.

Long Division Method
Using Euclid's Algorithm
Prime Factorization Method

GCF of 20 and 27 by Long Division

GCF of 20 and 27 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 27 (larger number) by 20 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (20) by the remainder (7).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 20 and 27.

GCF of 20 and 27 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 = 27 and Y = 20

GCF(27, 20) = GCF(20, 27 mod 20) = GCF(20, 7)
GCF(20, 7) = GCF(7, 20 mod 7) = GCF(7, 6)
GCF(7, 6) = GCF(6, 7 mod 6) = GCF(6, 1)
GCF(6, 1) = 1 (∵ GCF(X, 1) = 1)

Therefore, the value of GCF of 20 and 27 is 1.

GCF of 20 and 27 by Prime Factorization

Prime factorization of 20 and 27 is (2 × 2 × 5) and (3 × 3 × 3) respectively. As visible, there are no common prime factors between 20 and 27, i.e. they are co-prime. Hence, the GCF of 20 and 27 will be 1.

☛ Also Check:

GCF of 20 and 27 Examples

Example 1: Find the GCF of 20 and 27, if their LCM is 540.

Solution:

∵ LCM × GCF = 20 × 27
⇒ GCF(20, 27) = (20 × 27)/540 = 1
Therefore, the greatest common factor of 20 and 27 is 1.
Example 2: The product of two numbers is 540. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 540
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 540/1
Therefore, the LCM is 540.
Example 3: For two numbers, GCF = 1 and LCM = 540. If one number is 20, find the other number.

Solution:

Given: GCF (z, 20) = 1 and LCM (z, 20) = 540
∵ GCF × LCM = 20 × (z)
⇒ z = (GCF × LCM)/20
⇒ z = (1 × 540)/20
⇒ z = 27
Therefore, the other number is 27.

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FAQs on GCF of 20 and 27

What is the GCF of 20 and 27?

The GCF of 20 and 27 is 1. To calculate the GCF of 20 and 27, we need to factor each number (factors of 20 = 1, 2, 4, 5, 10, 20; factors of 27 = 1, 3, 9, 27) and choose the greatest factor that exactly divides both 20 and 27, i.e., 1.

If the GCF of 27 and 20 is 1, Find its LCM.

GCF(27, 20) × LCM(27, 20) = 27 × 20
Since the GCF of 27 and 20 = 1
⇒ 1 × LCM(27, 20) = 540
Therefore, LCM = 540
☛ GCF Calculator

What are the Methods to Find GCF of 20 and 27?

There are three commonly used methods to find the GCF of 20 and 27.

By Prime Factorization
By Long Division
By Euclidean Algorithm

How to Find the GCF of 20 and 27 by Prime Factorization?

To find the GCF of 20 and 27, we will find the prime factorization of the given numbers, i.e. 20 = 2 × 2 × 5; 27 = 3 × 3 × 3.
⇒ There is no common prime factor for 20 and 27. Hence, GCF (20, 27) = 1.
☛ Prime Number

What is the Relation Between LCM and GCF of 20, 27?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 20 and 27, i.e. GCF × LCM = 20 × 27.

How to Find the GCF of 20 and 27 by Long Division Method?

To find the GCF of 20, 27 using long division method, 27 is divided by 20. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

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