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HCF of 81 and 237

HCF of 81 and 237 is the largest possible number that divides 81 and 237 exactly without any remainder. The factors of 81 and 237 are 1, 3, 9, 27, 81 and 1, 3, 79, 237 respectively. There are 3 commonly used methods to find the HCF of 81 and 237 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 81 and 237
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 81 and 237?

Answer: HCF of 81 and 237 is 3.

Explanation:

The HCF of two non-zero integers, x(81) and y(237), is the highest positive integer m(3) that divides both x(81) and y(237) without any remainder.

Methods to Find HCF of 81 and 237

Let's look at the different methods for finding the HCF of 81 and 237.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

HCF of 81 and 237 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 = 237 and Y = 81

HCF(237, 81) = HCF(81, 237 mod 81) = HCF(81, 75)
HCF(81, 75) = HCF(75, 81 mod 75) = HCF(75, 6)
HCF(75, 6) = HCF(6, 75 mod 6) = HCF(6, 3)
HCF(6, 3) = HCF(3, 6 mod 3) = HCF(3, 0)
HCF(3, 0) = 3 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 81 and 237 is 3.

HCF of 81 and 237 by Long Division

HCF of 81 and 237 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 237 (larger number) by 81 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (81) by the remainder (75).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the HCF of 81 and 237.

HCF of 81 and 237 by Listing Common Factors

Factors of 81: 1, 3, 9, 27, 81
Factors of 237: 1, 3, 79, 237

There are 2 common factors of 81 and 237, that are 1 and 3. Therefore, the highest common factor of 81 and 237 is 3.

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HCF of 81 and 237 Examples

Example 1: Find the highest number that divides 81 and 237 exactly.

Solution:

The highest number that divides 81 and 237 exactly is their highest common factor, i.e. HCF of 81 and 237.
⇒ Factors of 81 and 237:
- Factors of 81 = 1, 3, 9, 27, 81
- Factors of 237 = 1, 3, 79, 237
Therefore, the HCF of 81 and 237 is 3.
Example 2: The product of two numbers is 19197. If their HCF is 3, what is their LCM?

Solution:

Given: HCF = 3 and product of numbers = 19197
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 19197/3
Therefore, the LCM is 6399.
Example 3: Find the HCF of 81 and 237, if their LCM is 6399.

Solution:

∵ LCM × HCF = 81 × 237
⇒ HCF(81, 237) = (81 × 237)/6399 = 3
Therefore, the highest common factor of 81 and 237 is 3.

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FAQs on HCF of 81 and 237

What is the HCF of 81 and 237?

The HCF of 81 and 237 is 3. To calculate the HCF of 81 and 237, we need to factor each number (factors of 81 = 1, 3, 9, 27, 81; factors of 237 = 1, 3, 79, 237) and choose the highest factor that exactly divides both 81 and 237, i.e., 3.

What is the Relation Between LCM and HCF of 81, 237?

The following equation can be used to express the relation between Least Common Multiple and HCF of 81 and 237, i.e. HCF × LCM = 81 × 237.

How to Find the HCF of 81 and 237 by Long Division Method?

To find the HCF of 81, 237 using long division method, 237 is divided by 81. The corresponding divisor (3) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 81 and 237?

There are three commonly used methods to find the HCF of 81 and 237.

By Listing Common Factors
By Long Division
By Prime Factorization

If the HCF of 237 and 81 is 3, Find its LCM.

HCF(237, 81) × LCM(237, 81) = 237 × 81
Since the HCF of 237 and 81 = 3
⇒ 3 × LCM(237, 81) = 19197
Therefore, LCM = 6399
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How to Find the HCF of 81 and 237 by Prime Factorization?

To find the HCF of 81 and 237, we will find the prime factorization of the given numbers, i.e. 81 = 3 × 3 × 3 × 3; 237 = 3 × 79.
⇒ Since 3 is the only common prime factor of 81 and 237. Hence, HCF (81, 237) = 3.
☛ Prime Number

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