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HCF of 14 and 21

HCF of 14 and 21 is the largest possible number that divides 14 and 21 exactly without any remainder. The factors of 14 and 21 are 1, 2, 7, 14 and 1, 3, 7, 21 respectively. There are 3 commonly used methods to find the HCF of 14 and 21 - long division, prime factorization, and Euclidean algorithm.

1.	HCF of 14 and 21
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 14 and 21?

Answer: HCF of 14 and 21 is 7.

Explanation:

The HCF of two non-zero integers, x(14) and y(21), is the highest positive integer m(7) that divides both x(14) and y(21) without any remainder.

Methods to Find HCF of 14 and 21

Let's look at the different methods for finding the HCF of 14 and 21.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

HCF of 14 and 21 by Long Division

HCF of 14 and 21 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 21 (larger number) by 14 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (14) by the remainder (7).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (7) is the HCF of 14 and 21.

HCF of 14 and 21 by Prime Factorization

Prime factorization of 14 and 21 is (2 × 7) and (3 × 7) respectively. As visible, 14 and 21 have only one common prime factor i.e. 7. Hence, the HCF of 14 and 21 is 7.

HCF of 14 and 21 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 = 21 and Y = 14

HCF(21, 14) = HCF(14, 21 mod 14) = HCF(14, 7)
HCF(14, 7) = HCF(7, 14 mod 7) = HCF(7, 0)
HCF(7, 0) = 7 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 14 and 21 is 7.

☛ Also Check:

HCF of 14 and 21 Examples

Example 1: For two numbers, HCF = 7 and LCM = 42. If one number is 21, find the other number.

Solution:

Given: HCF (z, 21) = 7 and LCM (z, 21) = 42
∵ HCF × LCM = 21 × (z)
⇒ z = (HCF × LCM)/21
⇒ z = (7 × 42)/21
⇒ z = 14
Therefore, the other number is 14.
Example 2: The product of two numbers is 294. If their HCF is 7, what is their LCM?

Solution:

Given: HCF = 7 and product of numbers = 294
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 294/7
Therefore, the LCM is 42.
Example 3: Find the HCF of 14 and 21, if their LCM is 42.

Solution:

∵ LCM × HCF = 14 × 21
⇒ HCF(14, 21) = (14 × 21)/42 = 7
Therefore, the highest common factor of 14 and 21 is 7.

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FAQs on HCF of 14 and 21

What is the HCF of 14 and 21?

The HCF of 14 and 21 is 7. To calculate the HCF (Highest Common Factor) of 14 and 21, we need to factor each number (factors of 14 = 1, 2, 7, 14; factors of 21 = 1, 3, 7, 21) and choose the highest factor that exactly divides both 14 and 21, i.e., 7.

If the HCF of 21 and 14 is 7, Find its LCM.

HCF(21, 14) × LCM(21, 14) = 21 × 14
Since the HCF of 21 and 14 = 7
⇒ 7 × LCM(21, 14) = 294
Therefore, LCM = 42
☛ HCF Calculator

How to Find the HCF of 14 and 21 by Long Division Method?

To find the HCF of 14, 21 using long division method, 21 is divided by 14. The corresponding divisor (7) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 14 and 21?

There are three commonly used methods to find the HCF of 14 and 21.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the HCF of 14 and 21 by Prime Factorization?

To find the HCF of 14 and 21, we will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 21 = 3 × 7.
⇒ Since 7 is the only common prime factor of 14 and 21. Hence, HCF (14, 21) = 7.
☛ What are Prime Numbers?

What is the Relation Between LCM and HCF of 14, 21?

The following equation can be used to express the relation between LCM and HCF of 14 and 21, i.e. HCF × LCM = 14 × 21.

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