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GCF of 14 and 56

GCF of 14 and 56 is the largest possible number that divides 14 and 56 exactly without any remainder. The factors of 14 and 56 are 1, 2, 7, 14 and 1, 2, 4, 7, 8, 14, 28, 56 respectively. There are 3 commonly used methods to find the GCF of 14 and 56 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 14 and 56
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 14 and 56?

Answer: GCF of 14 and 56 is 14.

Explanation:

The GCF of two non-zero integers, x(14) and y(56), is the greatest positive integer m(14) that divides both x(14) and y(56) without any remainder.

Methods to Find GCF of 14 and 56

Let's look at the different methods for finding the GCF of 14 and 56.

Prime Factorization Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 14 and 56 by Prime Factorization

Prime factorization of 14 and 56 is (2 × 7) and (2 × 2 × 2 × 7) respectively. As visible, 14 and 56 have common prime factors. Hence, the GCF of 14 and 56 is 2 × 7 = 14.

GCF of 14 and 56 by Listing Common Factors

Factors of 14: 1, 2, 7, 14
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56

There are 4 common factors of 14 and 56, that are 1, 2, 14, and 7. Therefore, the greatest common factor of 14 and 56 is 14.

GCF of 14 and 56 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 = 56 and Y = 14

GCF(56, 14) = GCF(14, 56 mod 14) = GCF(14, 0)
GCF(14, 0) = 14 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 14 and 56 is 14.

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GCF of 14 and 56 Examples

Example 1: Find the greatest number that divides 14 and 56 exactly.

Solution:

The greatest number that divides 14 and 56 exactly is their greatest common factor, i.e. GCF of 14 and 56.
⇒ Factors of 14 and 56:
- Factors of 14 = 1, 2, 7, 14
- Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
Therefore, the GCF of 14 and 56 is 14.
Example 2: Find the GCF of 14 and 56, if their LCM is 56.

Solution:

∵ LCM × GCF = 14 × 56
⇒ GCF(14, 56) = (14 × 56)/56 = 14
Therefore, the greatest common factor of 14 and 56 is 14.
Example 3: For two numbers, GCF = 14 and LCM = 56. If one number is 56, find the other number.

Solution:

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

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FAQs on GCF of 14 and 56

What is the GCF of 14 and 56?

The GCF of 14 and 56 is 14. To calculate the GCF (Greatest Common Factor) of 14 and 56, we need to factor each number (factors of 14 = 1, 2, 7, 14; factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56) and choose the greatest factor that exactly divides both 14 and 56, i.e., 14.

If the GCF of 56 and 14 is 14, Find its LCM.

GCF(56, 14) × LCM(56, 14) = 56 × 14
Since the GCF of 56 and 14 = 14
⇒ 14 × LCM(56, 14) = 784
Therefore, LCM = 56
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How to Find the GCF of 14 and 56 by Long Division Method?

To find the GCF of 14, 56 using long division method, 56 is divided by 14. The corresponding divisor (14) when remainder equals 0 is taken as GCF.

How to Find the GCF of 14 and 56 by Prime Factorization?

To find the GCF of 14 and 56, we will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 56 = 2 × 2 × 2 × 7.
⇒ Since 2, 7 are common terms in the prime factorization of 14 and 56. Hence, GCF(14, 56) = 2 × 7 = 14
☛ What is a Prime Number?

What is the Relation Between LCM and GCF of 14, 56?

The following equation can be used to express the relation between LCM and GCF of 14 and 56, i.e. GCF × LCM = 14 × 56.

What are the Methods to Find GCF of 14 and 56?

There are three commonly used methods to find the GCF of 14 and 56.

By Prime Factorization
By Long Division
By Listing Common Factors

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