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HCF of 21 and 29

HCF of 21 and 29 is the largest possible number that divides 21 and 29 exactly without any remainder. The factors of 21 and 29 are 1, 3, 7, 21 and 1, 29 respectively. There are 3 commonly used methods to find the HCF of 21 and 29 - long division, prime factorization, and Euclidean algorithm.

1.	HCF of 21 and 29
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 21 and 29?

Answer: HCF of 21 and 29 is 1.

Explanation:

The HCF of two non-zero integers, x(21) and y(29), is the highest positive integer m(1) that divides both x(21) and y(29) without any remainder.

Methods to Find HCF of 21 and 29

Let's look at the different methods for finding the HCF of 21 and 29.

Using Euclid's Algorithm
Listing Common Factors
Long Division Method

HCF of 21 and 29 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 = 29 and Y = 21

HCF(29, 21) = HCF(21, 29 mod 21) = HCF(21, 8)
HCF(21, 8) = HCF(8, 21 mod 8) = HCF(8, 5)
HCF(8, 5) = HCF(5, 8 mod 5) = HCF(5, 3)
HCF(5, 3) = HCF(3, 5 mod 3) = HCF(3, 2)
HCF(3, 2) = HCF(2, 3 mod 2) = HCF(2, 1)
HCF(2, 1) = 1 (∵ HCF(X, 1) = 1)

Therefore, the value of HCF of 21 and 29 is 1.

HCF of 21 and 29 by Listing Common Factors

Factors of 21: 1, 3, 7, 21
Factors of 29: 1, 29

Since, 1 is the only common factor between 21 and 29. The highest common factor of 21 and 29 is 1.

HCF of 21 and 29 by Long Division

HCF of 21 and 29 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 29 (larger number) by 21 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (21) by the remainder (8).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the HCF of 21 and 29.

☛ Also Check:

HCF of 21 and 29 Examples

Example 1: The product of two numbers is 609. If their HCF is 1, what is their LCM?

Solution:

Given: HCF = 1 and product of numbers = 609
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 609/1
Therefore, the LCM is 609.
Example 2: Find the HCF of 21 and 29, if their LCM is 609.

Solution:

∵ LCM × HCF = 21 × 29
⇒ HCF(21, 29) = (21 × 29)/609 = 1
Therefore, the highest common factor of 21 and 29 is 1.
Example 3: For two numbers, HCF = 1 and LCM = 609. If one number is 29, find the other number.

Solution:

Given: HCF (y, 29) = 1 and LCM (y, 29) = 609
∵ HCF × LCM = 29 × (y)
⇒ y = (HCF × LCM)/29
⇒ y = (1 × 609)/29
⇒ y = 21
Therefore, the other number is 21.

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FAQs on HCF of 21 and 29

What is the HCF of 21 and 29?

The HCF of 21 and 29 is 1. To calculate the HCF (Highest Common Factor) of 21 and 29, we need to factor each number (factors of 21 = 1, 3, 7, 21; factors of 29 = 1, 29) and choose the highest factor that exactly divides both 21 and 29, i.e., 1.

What are the Methods to Find HCF of 21 and 29?

There are three commonly used methods to find the HCF of 21 and 29.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the HCF of 21 and 29 by Long Division Method?

To find the HCF of 21, 29 using long division method, 29 is divided by 21. The corresponding divisor (1) when remainder equals 0 is taken as HCF.

How to Find the HCF of 21 and 29 by Prime Factorization?

To find the HCF of 21 and 29, we will find the prime factorization of the given numbers, i.e. 21 = 3 × 7; 29 = 29.
⇒ There is no common prime factor for 21 and 29. Hence, HCF (21, 29) = 1.
☛ Prime Numbers

If the HCF of 29 and 21 is 1, Find its LCM.

HCF(29, 21) × LCM(29, 21) = 29 × 21
Since the HCF of 29 and 21 = 1
⇒ 1 × LCM(29, 21) = 609
Therefore, LCM = 609
☛ Highest Common Factor Calculator

What is the Relation Between LCM and HCF of 21, 29?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 21 and 29, i.e. HCF × LCM = 21 × 29.

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