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GCF of 6 and 12

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

1.	GCF of 6 and 12
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 6 and 12?

Answer: GCF of 6 and 12 is 6.

Explanation:

The GCF of two non-zero integers, x(6) and y(12), is the greatest positive integer m(6) that divides both x(6) and y(12) without any remainder.

Methods to Find GCF of 6 and 12

The methods to find the GCF of 6 and 12 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 6 and 12 by Long Division

GCF of 6 and 12 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 12 (larger number) by 6 (smaller number).
Step 2: Since the remainder = 0, the divisor (6) is the GCF of 6 and 12.

The corresponding divisor (6) is the GCF of 6 and 12.

GCF of 6 and 12 by Prime Factorization

Prime factorization of 6 and 12 is (2 × 3) and (2 × 2 × 3) respectively. As visible, 6 and 12 have common prime factors. Hence, the GCF of 6 and 12 is 2 × 3 = 6.

GCF of 6 and 12 by Listing Common Factors

Factors of 6: 1, 2, 3, 6
Factors of 12: 1, 2, 3, 4, 6, 12

There are 4 common factors of 6 and 12, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 6 and 12 is 6.

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GCF of 6 and 12 Examples

Example 1: Find the GCF of 6 and 12, if their LCM is 12.

Solution:

∵ LCM × GCF = 6 × 12
⇒ GCF(6, 12) = (6 × 12)/12 = 6
Therefore, the greatest common factor of 6 and 12 is 6.
Example 2: For two numbers, GCF = 6 and LCM = 12. If one number is 6, find the other number.

Solution:

Given: GCF (y, 6) = 6 and LCM (y, 6) = 12
∵ GCF × LCM = 6 × (y)
⇒ y = (GCF × LCM)/6
⇒ y = (6 × 12)/6
⇒ y = 12
Therefore, the other number is 12.
Example 3: The product of two numbers is 72. If their GCF is 6, what is their LCM?

Solution:

Given: GCF = 6 and product of numbers = 72
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 72/6
Therefore, the LCM is 12.

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FAQs on GCF of 6 and 12

What is the GCF of 6 and 12?

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

What is the Relation Between LCM and GCF of 6, 12?

The following equation can be used to express the relation between LCM and GCF of 6 and 12, i.e. GCF × LCM = 6 × 12.

If the GCF of 12 and 6 is 6, Find its LCM.

GCF(12, 6) × LCM(12, 6) = 12 × 6
Since the GCF of 12 and 6 = 6
⇒ 6 × LCM(12, 6) = 72
Therefore, LCM = 12
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What are the Methods to Find GCF of 6 and 12?

There are three commonly used methods to find the GCF of 6 and 12.

By Listing Common Factors
By Prime Factorization
By Long Division

How to Find the GCF of 6 and 12 by Long Division Method?

To find the GCF of 6, 12 using long division method, 12 is divided by 6. The corresponding divisor (6) when remainder equals 0 is taken as GCF.

How to Find the GCF of 6 and 12 by Prime Factorization?

To find the GCF of 6 and 12, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 12 = 2 × 2 × 3.
⇒ Since 2, 3 are common terms in the prime factorization of 6 and 12. Hence, GCF(6, 12) = 2 × 3 = 6
☛ What is a Prime Number?

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