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HCF of 609 and 957

HCF of 609 and 957 is the largest possible number that divides 609 and 957 exactly without any remainder. The factors of 609 and 957 are 1, 3, 7, 21, 29, 87, 203, 609 and 1, 3, 11, 29, 33, 87, 319, 957 respectively. There are 3 commonly used methods to find the HCF of 609 and 957 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 609 and 957
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 609 and 957?

Answer: HCF of 609 and 957 is 87.

Explanation:

The HCF of two non-zero integers, x(609) and y(957), is the highest positive integer m(87) that divides both x(609) and y(957) without any remainder.

Methods to Find HCF of 609 and 957

The methods to find the HCF of 609 and 957 are explained below.

Using Euclid's Algorithm
Listing Common Factors
Long Division Method

HCF of 609 and 957 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 = 957 and Y = 609

HCF(957, 609) = HCF(609, 957 mod 609) = HCF(609, 348)
HCF(609, 348) = HCF(348, 609 mod 348) = HCF(348, 261)
HCF(348, 261) = HCF(261, 348 mod 261) = HCF(261, 87)
HCF(261, 87) = HCF(87, 261 mod 87) = HCF(87, 0)
HCF(87, 0) = 87 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 609 and 957 is 87.

HCF of 609 and 957 by Listing Common Factors

Factors of 609: 1, 3, 7, 21, 29, 87, 203, 609
Factors of 957: 1, 3, 11, 29, 33, 87, 319, 957

There are 4 common factors of 609 and 957, that are 1, 3, 29, and 87. Therefore, the highest common factor of 609 and 957 is 87.

HCF of 609 and 957 by Long Division

HCF of 609 and 957 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 957 (larger number) by 609 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (609) by the remainder (348).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (87) is the HCF of 609 and 957.

☛ Also Check:

HCF of 609 and 957 Examples

Example 1: For two numbers, HCF = 87 and LCM = 6699. If one number is 609, find the other number.

Solution:

Given: HCF (x, 609) = 87 and LCM (x, 609) = 6699
∵ HCF × LCM = 609 × (x)
⇒ x = (HCF × LCM)/609
⇒ x = (87 × 6699)/609
⇒ x = 957
Therefore, the other number is 957.
Example 2: Find the highest number that divides 609 and 957 exactly.

Solution:

The highest number that divides 609 and 957 exactly is their highest common factor, i.e. HCF of 609 and 957.
⇒ Factors of 609 and 957:
- Factors of 609 = 1, 3, 7, 21, 29, 87, 203, 609
- Factors of 957 = 1, 3, 11, 29, 33, 87, 319, 957
Therefore, the HCF of 609 and 957 is 87.
Example 3: Find the HCF of 609 and 957, if their LCM is 6699.

Solution:

∵ LCM × HCF = 609 × 957
⇒ HCF(609, 957) = (609 × 957)/6699 = 87
Therefore, the highest common factor of 609 and 957 is 87.

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FAQs on HCF of 609 and 957

What is the HCF of 609 and 957?

The HCF of 609 and 957 is 87. To calculate the HCF (Highest Common Factor) of 609 and 957, we need to factor each number (factors of 609 = 1, 3, 7, 21, 29, 87, 203, 609; factors of 957 = 1, 3, 11, 29, 33, 87, 319, 957) and choose the highest factor that exactly divides both 609 and 957, i.e., 87.

What are the Methods to Find HCF of 609 and 957?

There are three commonly used methods to find the HCF of 609 and 957.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the HCF of 609 and 957 by Prime Factorization?

To find the HCF of 609 and 957, we will find the prime factorization of the given numbers, i.e. 609 = 3 × 7 × 29; 957 = 3 × 11 × 29.
⇒ Since 3, 29 are common terms in the prime factorization of 609 and 957. Hence, HCF(609, 957) = 3 × 29 = 87
☛ Prime Number

If the HCF of 957 and 609 is 87, Find its LCM.

HCF(957, 609) × LCM(957, 609) = 957 × 609
Since the HCF of 957 and 609 = 87
⇒ 87 × LCM(957, 609) = 582813
Therefore, LCM = 6699
☛ HCF Calculator

What is the Relation Between LCM and HCF of 609, 957?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 609 and 957, i.e. HCF × LCM = 609 × 957.

How to Find the HCF of 609 and 957 by Long Division Method?

To find the HCF of 609, 957 using long division method, 957 is divided by 609. The corresponding divisor (87) when remainder equals 0 is taken as HCF.

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