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GCF of 8 and 14

GCF of 8 and 14 is the largest possible number that divides 8 and 14 exactly without any remainder. The factors of 8 and 14 are 1, 2, 4, 8 and 1, 2, 7, 14 respectively. There are 3 commonly used methods to find the GCF of 8 and 14 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 8 and 14
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 8 and 14?

Answer: GCF of 8 and 14 is 2.

Explanation:

The GCF of two non-zero integers, x(8) and y(14), is the greatest positive integer m(2) that divides both x(8) and y(14) without any remainder.

Methods to Find GCF of 8 and 14

The methods to find the GCF of 8 and 14 are explained below.

Prime Factorization Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 8 and 14 by Prime Factorization

Prime factorization of 8 and 14 is (2 × 2 × 2) and (2 × 7) respectively. As visible, 8 and 14 have only one common prime factor i.e. 2. Hence, the GCF of 8 and 14 is 2.

GCF of 8 and 14 by Listing Common Factors

Factors of 8: 1, 2, 4, 8
Factors of 14: 1, 2, 7, 14

There are 2 common factors of 8 and 14, that are 1 and 2. Therefore, the greatest common factor of 8 and 14 is 2.

GCF of 8 and 14 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 = 14 and Y = 8

GCF(14, 8) = GCF(8, 14 mod 8) = GCF(8, 6)
GCF(8, 6) = GCF(6, 8 mod 6) = GCF(6, 2)
GCF(6, 2) = GCF(2, 6 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 8 and 14 is 2.

☛ Also Check:

GCF of 8 and 14 Examples

Example 1: Find the GCF of 8 and 14, if their LCM is 56.

Solution:

∵ LCM × GCF = 8 × 14
⇒ GCF(8, 14) = (8 × 14)/56 = 2
Therefore, the greatest common factor of 8 and 14 is 2.
Example 2: The product of two numbers is 112. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 112
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 112/2
Therefore, the LCM is 56.
Example 3: For two numbers, GCF = 2 and LCM = 56. If one number is 14, find the other number.

Solution:

Given: GCF (z, 14) = 2 and LCM (z, 14) = 56
∵ GCF × LCM = 14 × (z)
⇒ z = (GCF × LCM)/14
⇒ z = (2 × 56)/14
⇒ z = 8
Therefore, the other number is 8.

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FAQs on GCF of 8 and 14

What is the GCF of 8 and 14?

The GCF of 8 and 14 is 2. To calculate the GCF of 8 and 14, we need to factor each number (factors of 8 = 1, 2, 4, 8; factors of 14 = 1, 2, 7, 14) and choose the greatest factor that exactly divides both 8 and 14, i.e., 2.

What are the Methods to Find GCF of 8 and 14?

There are three commonly used methods to find the GCF of 8 and 14.

By Listing Common Factors
By Long Division
By Prime Factorization

How to Find the GCF of 8 and 14 by Prime Factorization?

To find the GCF of 8 and 14, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 14 = 2 × 7.
⇒ Since 2 is the only common prime factor of 8 and 14. Hence, GCF (8, 14) = 2.
☛ Prime Number

If the GCF of 14 and 8 is 2, Find its LCM.

GCF(14, 8) × LCM(14, 8) = 14 × 8
Since the GCF of 14 and 8 = 2
⇒ 2 × LCM(14, 8) = 112
Therefore, LCM = 56
☛ Greatest Common Factor Calculator

How to Find the GCF of 8 and 14 by Long Division Method?

To find the GCF of 8, 14 using long division method, 14 is divided by 8. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 8, 14?

The following equation can be used to express the relation between Least Common Multiple and GCF of 8 and 14, i.e. GCF × LCM = 8 × 14.

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