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GCF of 8 and 18

GCF of 8 and 18 is the largest possible number that divides 8 and 18 exactly without any remainder. The factors of 8 and 18 are 1, 2, 4, 8 and 1, 2, 3, 6, 9, 18 respectively. There are 3 commonly used methods to find the GCF of 8 and 18 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 8 and 18
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 8 and 18?

Answer: GCF of 8 and 18 is 2.

Explanation:

The GCF of two non-zero integers, x(8) and y(18), is the greatest positive integer m(2) that divides both x(8) and y(18) without any remainder.

Methods to Find GCF of 8 and 18

The methods to find the GCF of 8 and 18 are explained below.

Listing Common Factors
Prime Factorization Method
Using Euclid's Algorithm

GCF of 8 and 18 by Listing Common Factors

Factors of 8: 1, 2, 4, 8
Factors of 18: 1, 2, 3, 6, 9, 18

There are 2 common factors of 8 and 18, that are 1 and 2. Therefore, the greatest common factor of 8 and 18 is 2.

GCF of 8 and 18 by Prime Factorization

Prime factorization of 8 and 18 is (2 × 2 × 2) and (2 × 3 × 3) respectively. As visible, 8 and 18 have only one common prime factor i.e. 2. Hence, the GCF of 8 and 18 is 2.

GCF of 8 and 18 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 = 18 and Y = 8

GCF(18, 8) = GCF(8, 18 mod 8) = GCF(8, 2)
GCF(8, 2) = GCF(2, 8 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 8 and 18 is 2.

☛ Also Check:

GCF of 8 and 18 Examples

Example 1: For two numbers, GCF = 2 and LCM = 72. If one number is 18, find the other number.

Solution:

Given: GCF (x, 18) = 2 and LCM (x, 18) = 72
∵ GCF × LCM = 18 × (x)
⇒ x = (GCF × LCM)/18
⇒ x = (2 × 72)/18
⇒ x = 8
Therefore, the other number is 8.
Example 2: The product of two numbers is 144. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 144
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 144/2
Therefore, the LCM is 72.
Example 3: Find the GCF of 8 and 18, if their LCM is 72.

Solution:

∵ LCM × GCF = 8 × 18
⇒ GCF(8, 18) = (8 × 18)/72 = 2
Therefore, the greatest common factor of 8 and 18 is 2.

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FAQs on GCF of 8 and 18

What is the GCF of 8 and 18?

The GCF of 8 and 18 is 2. To calculate the greatest common factor of 8 and 18, we need to factor each number (factors of 8 = 1, 2, 4, 8; factors of 18 = 1, 2, 3, 6, 9, 18) and choose the greatest factor that exactly divides both 8 and 18, i.e., 2.

If the GCF of 18 and 8 is 2, Find its LCM.

GCF(18, 8) × LCM(18, 8) = 18 × 8
Since the GCF of 18 and 8 = 2
⇒ 2 × LCM(18, 8) = 144
Therefore, LCM = 72
☛ GCF Calculator

What are the Methods to Find GCF of 8 and 18?

There are three commonly used methods to find the GCF of 8 and 18.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 8 and 18 by Prime Factorization?

To find the GCF of 8 and 18, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 18 = 2 × 3 × 3.
⇒ Since 2 is the only common prime factor of 8 and 18. Hence, GCF (8, 18) = 2.
☛ What is a Prime Number?

What is the Relation Between LCM and GCF of 8, 18?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 8 and 18, i.e. GCF × LCM = 8 × 18.

How to Find the GCF of 8 and 18 by Long Division Method?

To find the GCF of 8, 18 using long division method, 18 is divided by 8. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

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