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GCF of 12 and 14

GCF of 12 and 14 is the largest possible number that divides 12 and 14 exactly without any remainder. The factors of 12 and 14 are 1, 2, 3, 4, 6, 12 and 1, 2, 7, 14 respectively. There are 3 commonly used methods to find the GCF of 12 and 14 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 12 and 14
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 12 and 14?

Answer: GCF of 12 and 14 is 2.

Explanation:

The GCF of two non-zero integers, x(12) and y(14), is the greatest positive integer m(2) that divides both x(12) and y(14) without any remainder.

Methods to Find GCF of 12 and 14

The methods to find the GCF of 12 and 14 are explained below.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

GCF of 12 and 14 by Long Division

GCF of 12 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 12 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 12 and 14.

GCF of 12 and 14 by Prime Factorization

Prime factorization of 12 and 14 is (2 × 2 × 3) and (2 × 7) respectively. As visible, 12 and 14 have only one common prime factor i.e. 2. Hence, the GCF of 12 and 14 is 2.

GCF of 12 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 = 12

GCF(14, 12) = GCF(12, 14 mod 12) = GCF(12, 2)
GCF(12, 2) = GCF(2, 12 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 12 and 14 is 2.

☛ Also Check:

GCF of 12 and 14 Examples

Example 1: Find the GCF of 12 and 14, if their LCM is 84.

Solution:

∵ LCM × GCF = 12 × 14
⇒ GCF(12, 14) = (12 × 14)/84 = 2
Therefore, the greatest common factor of 12 and 14 is 2.
Example 2: For two numbers, GCF = 2 and LCM = 84. If one number is 14, find the other number.

Solution:

Given: GCF (z, 14) = 2 and LCM (z, 14) = 84
∵ GCF × LCM = 14 × (z)
⇒ z = (GCF × LCM)/14
⇒ z = (2 × 84)/14
⇒ z = 12
Therefore, the other number is 12.
Example 3: The product of two numbers is 168. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 168
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 168/2
Therefore, the LCM is 84.

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FAQs on GCF of 12 and 14

What is the GCF of 12 and 14?

The GCF of 12 and 14 is 2. To calculate the greatest common factor of 12 and 14, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 14 = 1, 2, 7, 14) and choose the greatest factor that exactly divides both 12 and 14, i.e., 2.

If the GCF of 14 and 12 is 2, Find its LCM.

GCF(14, 12) × LCM(14, 12) = 14 × 12
Since the GCF of 14 and 12 = 2
⇒ 2 × LCM(14, 12) = 168
Therefore, LCM = 84
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What is the Relation Between LCM and GCF of 12, 14?

The following equation can be used to express the relation between Least Common Multiple and GCF of 12 and 14, i.e. GCF × LCM = 12 × 14.

What are the Methods to Find GCF of 12 and 14?

There are three commonly used methods to find the GCF of 12 and 14.

By Long Division
By Prime Factorization
By Euclidean Algorithm

How to Find the GCF of 12 and 14 by Long Division Method?

To find the GCF of 12, 14 using long division method, 14 is divided by 12. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

How to Find the GCF of 12 and 14 by Prime Factorization?

To find the GCF of 12 and 14, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 14 = 2 × 7.
⇒ Since 2 is the only common prime factor of 12 and 14. Hence, GCF (12, 14) = 2.
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