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GCF of 6 and 18

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

1.	GCF of 6 and 18
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 6 and 18?

Answer: GCF of 6 and 18 is 6.

Explanation:

The GCF of two non-zero integers, x(6) and y(18), is the greatest positive integer m(6) that divides both x(6) and y(18) without any remainder.

Methods to Find GCF of 6 and 18

The methods to find the GCF of 6 and 18 are explained below.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 6 and 18 by Long Division

GCF of 6 and 18 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 18 (larger number) by 6 (smaller number).
Step 2: Since the remainder = 0, the divisor (6) is the GCF of 6 and 18.

The corresponding divisor (6) is the GCF of 6 and 18.

GCF of 6 and 18 by Listing Common Factors

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

There are 4 common factors of 6 and 18, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 6 and 18 is 6.

GCF of 6 and 18 by Prime Factorization

Prime factorization of 6 and 18 is (2 × 3) and (2 × 3 × 3) respectively. As visible, 6 and 18 have common prime factors. Hence, the GCF of 6 and 18 is 2 × 3 = 6.

☛ Also Check:

GCF of 6 and 18 Examples

Example 1: Find the greatest number that divides 6 and 18 exactly.

Solution:

The greatest number that divides 6 and 18 exactly is their greatest common factor, i.e. GCF of 6 and 18.
⇒ Factors of 6 and 18:
- Factors of 6 = 1, 2, 3, 6
- Factors of 18 = 1, 2, 3, 6, 9, 18
Therefore, the GCF of 6 and 18 is 6.
Example 2: For two numbers, GCF = 6 and LCM = 18. If one number is 18, find the other number.

Solution:

Given: GCF (x, 18) = 6 and LCM (x, 18) = 18
∵ GCF × LCM = 18 × (x)
⇒ x = (GCF × LCM)/18
⇒ x = (6 × 18)/18
⇒ x = 6
Therefore, the other number is 6.
Example 3: Find the GCF of 6 and 18, if their LCM is 18.

Solution:

∵ LCM × GCF = 6 × 18
⇒ GCF(6, 18) = (6 × 18)/18 = 6
Therefore, the greatest common factor of 6 and 18 is 6.

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FAQs on GCF of 6 and 18

What is the GCF of 6 and 18?

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

How to Find the GCF of 6 and 18 by Long Division Method?

To find the GCF of 6, 18 using long division method, 18 is divided by 6. The corresponding divisor (6) when remainder equals 0 is taken as GCF.

How to Find the GCF of 6 and 18 by Prime Factorization?

To find the GCF of 6 and 18, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 18 = 2 × 3 × 3.
⇒ Since 2, 3 are common terms in the prime factorization of 6 and 18. Hence, GCF(6, 18) = 2 × 3 = 6
☛ Prime Numbers

What is the Relation Between LCM and GCF of 6, 18?

The following equation can be used to express the relation between LCM and GCF of 6 and 18, i.e. GCF × LCM = 6 × 18.

If the GCF of 18 and 6 is 6, Find its LCM.

GCF(18, 6) × LCM(18, 6) = 18 × 6
Since the GCF of 18 and 6 = 6
⇒ 6 × LCM(18, 6) = 108
Therefore, LCM = 18
☛ GCF Calculator

What are the Methods to Find GCF of 6 and 18?

There are three commonly used methods to find the GCF of 6 and 18.

By Listing Common Factors
By Prime Factorization
By Long Division

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