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GCF of 6 and 14

GCF of 6 and 14 is the largest possible number that divides 6 and 14 exactly without any remainder. The factors of 6 and 14 are 1, 2, 3, 6 and 1, 2, 7, 14 respectively. There are 3 commonly used methods to find the GCF of 6 and 14 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 6 and 14
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 6 and 14?

Answer: GCF of 6 and 14 is 2.

Explanation:

The GCF of two non-zero integers, x(6) and y(14), is the greatest positive integer m(2) that divides both x(6) and y(14) without any remainder.

Methods to Find GCF of 6 and 14

The methods to find the GCF of 6 and 14 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 6 and 14 by Prime Factorization

Prime factorization of 6 and 14 is (2 × 3) and (2 × 7) respectively. As visible, 6 and 14 have only one common prime factor i.e. 2. Hence, the GCF of 6 and 14 is 2.

GCF of 6 and 14 by Listing Common Factors

Factors of 6: 1, 2, 3, 6
Factors of 14: 1, 2, 7, 14

There are 2 common factors of 6 and 14, that are 1 and 2. Therefore, the greatest common factor of 6 and 14 is 2.

GCF of 6 and 14 by Long Division

GCF of 6 and 14 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 14 (larger number) by 6 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (6) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 6 and 14.

☛ Also Check:

GCF of 6 and 14 Examples

Example 1: Find the GCF of 6 and 14, if their LCM is 42.

Solution:

∵ LCM × GCF = 6 × 14
⇒ GCF(6, 14) = (6 × 14)/42 = 2
Therefore, the greatest common factor of 6 and 14 is 2.
Example 2: The product of two numbers is 84. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 84
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 84/2
Therefore, the LCM is 42.
Example 3: For two numbers, GCF = 2 and LCM = 42. If one number is 6, find the other number.

Solution:

Given: GCF (z, 6) = 2 and LCM (z, 6) = 42
∵ GCF × LCM = 6 × (z)
⇒ z = (GCF × LCM)/6
⇒ z = (2 × 42)/6
⇒ z = 14
Therefore, the other number is 14.

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FAQs on GCF of 6 and 14

What is the GCF of 6 and 14?

The GCF of 6 and 14 is 2. To calculate the greatest common factor (GCF) of 6 and 14, we need to factor each number (factors of 6 = 1, 2, 3, 6; factors of 14 = 1, 2, 7, 14) and choose the greatest factor that exactly divides both 6 and 14, i.e., 2.

If the GCF of 14 and 6 is 2, Find its LCM.

GCF(14, 6) × LCM(14, 6) = 14 × 6
Since the GCF of 14 and 6 = 2
⇒ 2 × LCM(14, 6) = 84
Therefore, LCM = 42
☛ Greatest Common Factor Calculator

How to Find the GCF of 6 and 14 by Long Division Method?

To find the GCF of 6, 14 using long division method, 14 is divided by 6. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 6, 14?

The following equation can be used to express the relation between Least Common Multiple and GCF of 6 and 14, i.e. GCF × LCM = 6 × 14.

How to Find the GCF of 6 and 14 by Prime Factorization?

To find the GCF of 6 and 14, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 14 = 2 × 7.
⇒ Since 2 is the only common prime factor of 6 and 14. Hence, GCF (6, 14) = 2.
☛ Prime Numbers

What are the Methods to Find GCF of 6 and 14?

There are three commonly used methods to find the GCF of 6 and 14.

By Prime Factorization
By Euclidean Algorithm
By Long Division

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