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GCF of 2 and 14

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

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

What is GCF of 2 and 14?

Answer: GCF of 2 and 14 is 2.

Explanation:

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

Methods to Find GCF of 2 and 14

Let's look at the different methods for finding the GCF of 2 and 14.

Long Division Method
Using Euclid's Algorithm
Prime Factorization Method

GCF of 2 and 14 by Long Division

GCF of 2 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 2 (smaller number).
Step 2: Since the remainder = 0, the divisor (2) is the GCF of 2 and 14.

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

GCF of 2 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 = 2

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

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

GCF of 2 and 14 by Prime Factorization

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

☛ Also Check:

GCF of 2 and 14 Examples

Example 1: Find the greatest number that divides 2 and 14 exactly.

Solution:

The greatest number that divides 2 and 14 exactly is their greatest common factor, i.e. GCF of 2 and 14.
⇒ Factors of 2 and 14:
- Factors of 2 = 1, 2
- Factors of 14 = 1, 2, 7, 14
Therefore, the GCF of 2 and 14 is 2.
Example 2: The product of two numbers is 28. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 28
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 28/2
Therefore, the LCM is 14.
Example 3: Find the GCF of 2 and 14, if their LCM is 14.

Solution:

∵ LCM × GCF = 2 × 14
⇒ GCF(2, 14) = (2 × 14)/14 = 2
Therefore, the greatest common factor of 2 and 14 is 2.

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FAQs on GCF of 2 and 14

What is the GCF of 2 and 14?

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

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

GCF(14, 2) × LCM(14, 2) = 14 × 2
Since the GCF of 14 and 2 = 2
⇒ 2 × LCM(14, 2) = 28
Therefore, LCM = 14
☛ GCF Calculator

What are the Methods to Find GCF of 2 and 14?

There are three commonly used methods to find the GCF of 2 and 14.

By Long Division
By Prime Factorization
By Euclidean Algorithm

What is the Relation Between LCM and GCF of 2, 14?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 2 and 14, i.e. GCF × LCM = 2 × 14.

How to Find the GCF of 2 and 14 by Prime Factorization?

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

How to Find the GCF of 2 and 14 by Long Division Method?

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

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