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HCF of 4 and 14

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

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

What is HCF of 4 and 14?

Answer: HCF of 4 and 14 is 2.

Explanation:

The HCF of two non-zero integers, x(4) and y(14), is the highest positive integer m(2) that divides both x(4) and y(14) without any remainder.

Methods to Find HCF of 4 and 14

The methods to find the HCF of 4 and 14 are explained below.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

HCF of 4 and 14 by Long Division

HCF of 4 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 4 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (4) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the HCF of 4 and 14.

HCF of 4 and 14 by Prime Factorization

Prime factorization of 4 and 14 is (2 × 2) and (2 × 7) respectively. As visible, 4 and 14 have only one common prime factor i.e. 2. Hence, the HCF of 4 and 14 is 2.

HCF of 4 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 = 4

HCF(14, 4) = HCF(4, 14 mod 4) = HCF(4, 2)
HCF(4, 2) = HCF(2, 4 mod 2) = HCF(2, 0)
HCF(2, 0) = 2 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 4 and 14 is 2.

☛ Also Check:

HCF of 4 and 14 Examples

Example 1: Find the HCF of 4 and 14, if their LCM is 28.

Solution:

∵ LCM × HCF = 4 × 14
⇒ HCF(4, 14) = (4 × 14)/28 = 2
Therefore, the highest common factor of 4 and 14 is 2.
Example 2: The product of two numbers is 56. If their HCF is 2, what is their LCM?

Solution:

Given: HCF = 2 and product of numbers = 56
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 56/2
Therefore, the LCM is 28.
Example 3: For two numbers, HCF = 2 and LCM = 28. If one number is 14, find the other number.

Solution:

Given: HCF (x, 14) = 2 and LCM (x, 14) = 28
∵ HCF × LCM = 14 × (x)
⇒ x = (HCF × LCM)/14
⇒ x = (2 × 28)/14
⇒ x = 4
Therefore, the other number is 4.

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FAQs on HCF of 4 and 14

What is the HCF of 4 and 14?

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

What are the Methods to Find HCF of 4 and 14?

There are three commonly used methods to find the HCF of 4 and 14.

By Long Division
By Prime Factorization
By Euclidean Algorithm

How to Find the HCF of 4 and 14 by Prime Factorization?

To find the HCF of 4 and 14, we will find the prime factorization of the given numbers, i.e. 4 = 2 × 2; 14 = 2 × 7.
⇒ Since 2 is the only common prime factor of 4 and 14. Hence, HCF (4, 14) = 2.
☛ Prime Numbers

How to Find the HCF of 4 and 14 by Long Division Method?

To find the HCF of 4, 14 using long division method, 14 is divided by 4. The corresponding divisor (2) when remainder equals 0 is taken as HCF.

If the HCF of 14 and 4 is 2, Find its LCM.

HCF(14, 4) × LCM(14, 4) = 14 × 4
Since the HCF of 14 and 4 = 2
⇒ 2 × LCM(14, 4) = 56
Therefore, LCM = 28
☛ HCF Calculator

What is the Relation Between LCM and HCF of 4, 14?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 4 and 14, i.e. HCF × LCM = 4 × 14.

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