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HCF of 12 and 14

HCF 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 HCF of 12 and 14 - Euclidean algorithm, long division, and prime factorization.

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

What is HCF of 12 and 14?

Answer: HCF of 12 and 14 is 2.

Explanation:

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

Methods to Find HCF of 12 and 14

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

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

HCF of 12 and 14 by Long Division

HCF 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 HCF of 12 and 14.

HCF of 12 and 14 by Listing Common Factors

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 14: 1, 2, 7, 14

There are 2 common factors of 12 and 14, that are 1 and 2. Therefore, the highest common factor of 12 and 14 is 2.

HCF of 12 and 14 by Euclidean Algorithm

As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 14 and Y = 12

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

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

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HCF of 12 and 14 Examples

Example 1: The product of two numbers is 168. If their HCF is 2, what is their LCM?

Solution:

Given: HCF = 2 and product of numbers = 168
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 168/2
Therefore, the LCM is 84.
Example 2: For two numbers, HCF = 2 and LCM = 84. If one number is 14, find the other number.

Solution:

Given: HCF (x, 14) = 2 and LCM (x, 14) = 84
∵ HCF × LCM = 14 × (x)
⇒ x = (HCF × LCM)/14
⇒ x = (2 × 84)/14
⇒ x = 12
Therefore, the other number is 12.
Example 3: Find the HCF of 12 and 14, if their LCM is 84.

Solution:

∵ LCM × HCF = 12 × 14
⇒ HCF(12, 14) = (12 × 14)/84 = 2
Therefore, the highest common factor of 12 and 14 is 2.

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FAQs on HCF of 12 and 14

What is the HCF of 12 and 14?

The HCF of 12 and 14 is 2. To calculate the Highest common factor (HCF) 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 highest factor that exactly divides both 12 and 14, i.e., 2.

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

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

By Euclidean Algorithm
By Prime Factorization
By Long Division

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

HCF(14, 12) × LCM(14, 12) = 14 × 12
Since the HCF of 14 and 12 = 2
⇒ 2 × LCM(14, 12) = 168
Therefore, LCM = 84
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How to Find the HCF of 12 and 14 by Long Division Method?

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

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

To find the HCF 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, HCF (12, 14) = 2.
☛ What are Prime Numbers?

What is the Relation Between LCM and HCF of 12, 14?

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

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