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GCF of 18 and 20

GCF of 18 and 20 is the largest possible number that divides 18 and 20 exactly without any remainder. The factors of 18 and 20 are 1, 2, 3, 6, 9, 18 and 1, 2, 4, 5, 10, 20 respectively. There are 3 commonly used methods to find the GCF of 18 and 20 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 18 and 20
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 18 and 20?

Answer: GCF of 18 and 20 is 2.

Explanation:

The GCF of two non-zero integers, x(18) and y(20), is the greatest positive integer m(2) that divides both x(18) and y(20) without any remainder.

Methods to Find GCF of 18 and 20

The methods to find the GCF of 18 and 20 are explained below.

Listing Common Factors
Prime Factorization Method
Using Euclid's Algorithm

GCF of 18 and 20 by Listing Common Factors

Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 20: 1, 2, 4, 5, 10, 20

There are 2 common factors of 18 and 20, that are 1 and 2. Therefore, the greatest common factor of 18 and 20 is 2.

GCF of 18 and 20 by Prime Factorization

Prime factorization of 18 and 20 is (2 × 3 × 3) and (2 × 2 × 5) respectively. As visible, 18 and 20 have only one common prime factor i.e. 2. Hence, the GCF of 18 and 20 is 2.

GCF of 18 and 20 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 = 20 and Y = 18

GCF(20, 18) = GCF(18, 20 mod 18) = GCF(18, 2)
GCF(18, 2) = GCF(2, 18 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 18 and 20 is 2.

☛ Also Check:

GCF of 18 and 20 Examples

Example 1: Find the GCF of 18 and 20, if their LCM is 180.

Solution:

∵ LCM × GCF = 18 × 20
⇒ GCF(18, 20) = (18 × 20)/180 = 2
Therefore, the greatest common factor of 18 and 20 is 2.
Example 2: The product of two numbers is 360. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 360
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 360/2
Therefore, the LCM is 180.
Example 3: For two numbers, GCF = 2 and LCM = 180. If one number is 20, find the other number.

Solution:

Given: GCF (z, 20) = 2 and LCM (z, 20) = 180
∵ GCF × LCM = 20 × (z)
⇒ z = (GCF × LCM)/20
⇒ z = (2 × 180)/20
⇒ z = 18
Therefore, the other number is 18.

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FAQs on GCF of 18 and 20

What is the GCF of 18 and 20?

The GCF of 18 and 20 is 2. To calculate the greatest common factor (GCF) of 18 and 20, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 20 = 1, 2, 4, 5, 10, 20) and choose the greatest factor that exactly divides both 18 and 20, i.e., 2.

How to Find the GCF of 18 and 20 by Prime Factorization?

To find the GCF of 18 and 20, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 20 = 2 × 2 × 5.
⇒ Since 2 is the only common prime factor of 18 and 20. Hence, GCF (18, 20) = 2.
☛ Prime Number

What is the Relation Between LCM and GCF of 18, 20?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 18 and 20, i.e. GCF × LCM = 18 × 20.

What are the Methods to Find GCF of 18 and 20?

There are three commonly used methods to find the GCF of 18 and 20.

By Prime Factorization
By Long Division
By Listing Common Factors

How to Find the GCF of 18 and 20 by Long Division Method?

To find the GCF of 18, 20 using long division method, 20 is divided by 18. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

If the GCF of 20 and 18 is 2, Find its LCM.

GCF(20, 18) × LCM(20, 18) = 20 × 18
Since the GCF of 20 and 18 = 2
⇒ 2 × LCM(20, 18) = 360
Therefore, LCM = 180
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