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GCF of 14 and 20

GCF of 14 and 20 is the largest possible number that divides 14 and 20 exactly without any remainder. The factors of 14 and 20 are 1, 2, 7, 14 and 1, 2, 4, 5, 10, 20 respectively. There are 3 commonly used methods to find the GCF of 14 and 20 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 14 and 20
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 14 and 20?

Answer: GCF of 14 and 20 is 2.

Explanation:

The GCF of two non-zero integers, x(14) and y(20), is the greatest positive integer m(2) that divides both x(14) and y(20) without any remainder.

Methods to Find GCF of 14 and 20

The methods to find the GCF of 14 and 20 are explained below.

Prime Factorization Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 14 and 20 by Prime Factorization

Prime factorization of 14 and 20 is (2 × 7) and (2 × 2 × 5) respectively. As visible, 14 and 20 have only one common prime factor i.e. 2. Hence, the GCF of 14 and 20 is 2.

GCF of 14 and 20 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 = 20 and Y = 14

GCF(20, 14) = GCF(14, 20 mod 14) = GCF(14, 6)
GCF(14, 6) = GCF(6, 14 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 14 and 20 is 2.

GCF of 14 and 20 by Listing Common Factors

Factors of 14: 1, 2, 7, 14
Factors of 20: 1, 2, 4, 5, 10, 20

There are 2 common factors of 14 and 20, that are 1 and 2. Therefore, the greatest common factor of 14 and 20 is 2.

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GCF of 14 and 20 Examples

Example 1: The product of two numbers is 280. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 280
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 280/2
Therefore, the LCM is 140.
Example 2: Find the GCF of 14 and 20, if their LCM is 140.

Solution:

∵ LCM × GCF = 14 × 20
⇒ GCF(14, 20) = (14 × 20)/140 = 2
Therefore, the greatest common factor of 14 and 20 is 2.
Example 3: Find the greatest number that divides 14 and 20 exactly.

Solution:

The greatest number that divides 14 and 20 exactly is their greatest common factor, i.e. GCF of 14 and 20.
⇒ Factors of 14 and 20:
- Factors of 14 = 1, 2, 7, 14
- Factors of 20 = 1, 2, 4, 5, 10, 20
Therefore, the GCF of 14 and 20 is 2.

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FAQs on GCF of 14 and 20

What is the GCF of 14 and 20?

The GCF of 14 and 20 is 2. To calculate the GCF of 14 and 20, we need to factor each number (factors of 14 = 1, 2, 7, 14; factors of 20 = 1, 2, 4, 5, 10, 20) and choose the greatest factor that exactly divides both 14 and 20, i.e., 2.

How to Find the GCF of 14 and 20 by Long Division Method?

To find the GCF of 14, 20 using long division method, 20 is divided by 14. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

If the GCF of 20 and 14 is 2, Find its LCM.

GCF(20, 14) × LCM(20, 14) = 20 × 14
Since the GCF of 20 and 14 = 2
⇒ 2 × LCM(20, 14) = 280
Therefore, LCM = 140
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 14 and 20?

There are three commonly used methods to find the GCF of 14 and 20.

By Prime Factorization
By Euclidean Algorithm
By Long Division

What is the Relation Between LCM and GCF of 14, 20?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 14 and 20, i.e. GCF × LCM = 14 × 20.

How to Find the GCF of 14 and 20 by Prime Factorization?

To find the GCF of 14 and 20, we will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 20 = 2 × 2 × 5.
⇒ Since 2 is the only common prime factor of 14 and 20. Hence, GCF (14, 20) = 2.
☛ What is a Prime Number?

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