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HCF of 306 and 657

HCF of 306 and 657 is the largest possible number that divides 306 and 657 exactly without any remainder. The factors of 306 and 657 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306 and 1, 3, 9, 73, 219, 657 respectively. There are 3 commonly used methods to find the HCF of 306 and 657 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 306 and 657
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 306 and 657?

Answer: HCF of 306 and 657 is 9.

Explanation:

The HCF of two non-zero integers, x(306) and y(657), is the highest positive integer m(9) that divides both x(306) and y(657) without any remainder.

Methods to Find HCF of 306 and 657

The methods to find the HCF of 306 and 657 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

HCF of 306 and 657 by Prime Factorization

Prime factorization of 306 and 657 is (2 × 3 × 3 × 17) and (3 × 3 × 73) respectively. As visible, 306 and 657 have common prime factors. Hence, the HCF of 306 and 657 is 3 × 3 = 9.

HCF of 306 and 657 by Listing Common Factors

Factors of 306: 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
Factors of 657: 1, 3, 9, 73, 219, 657

There are 3 common factors of 306 and 657, that are 1, 3, and 9. Therefore, the highest common factor of 306 and 657 is 9.

HCF of 306 and 657 by Long Division

HCF of 306 and 657 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 657 (larger number) by 306 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (306) by the remainder (45).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (9) is the HCF of 306 and 657.

☛ Also Check:

HCF of 306 and 657 Examples

Example 1: For two numbers, HCF = 9 and LCM = 22338. If one number is 657, find the other number.

Solution:

Given: HCF (y, 657) = 9 and LCM (y, 657) = 22338
∵ HCF × LCM = 657 × (y)
⇒ y = (HCF × LCM)/657
⇒ y = (9 × 22338)/657
⇒ y = 306
Therefore, the other number is 306.
Example 2: The product of two numbers is 201042. If their HCF is 9, what is their LCM?

Solution:

Given: HCF = 9 and product of numbers = 201042
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 201042/9
Therefore, the LCM is 22338.
Example 3: Find the highest number that divides 306 and 657 exactly.

Solution:

The highest number that divides 306 and 657 exactly is their highest common factor, i.e. HCF of 306 and 657.
⇒ Factors of 306 and 657:
- Factors of 306 = 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
- Factors of 657 = 1, 3, 9, 73, 219, 657
Therefore, the HCF of 306 and 657 is 9.

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FAQs on HCF of 306 and 657

What is the HCF of 306 and 657?

The HCF of 306 and 657 is 9. To calculate the Highest common factor of 306 and 657, we need to factor each number (factors of 306 = 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306; factors of 657 = 1, 3, 9, 73, 219, 657) and choose the highest factor that exactly divides both 306 and 657, i.e., 9.

What is the Relation Between LCM and HCF of 306, 657?

The following equation can be used to express the relation between LCM and HCF of 306 and 657, i.e. HCF × LCM = 306 × 657.

What are the Methods to Find HCF of 306 and 657?

There are three commonly used methods to find the HCF of 306 and 657.

By Listing Common Factors
By Long Division
By Prime Factorization

If the HCF of 657 and 306 is 9, Find its LCM.

HCF(657, 306) × LCM(657, 306) = 657 × 306
Since the HCF of 657 and 306 = 9
⇒ 9 × LCM(657, 306) = 201042
Therefore, LCM = 22338
☛ HCF Calculator

How to Find the HCF of 306 and 657 by Prime Factorization?

To find the HCF of 306 and 657, we will find the prime factorization of the given numbers, i.e. 306 = 2 × 3 × 3 × 17; 657 = 3 × 3 × 73.
⇒ Since 3, 3 are common terms in the prime factorization of 306 and 657. Hence, HCF(306, 657) = 3 × 3 = 9
☛ Prime Number

How to Find the HCF of 306 and 657 by Long Division Method?

To find the HCF of 306, 657 using long division method, 657 is divided by 306. The corresponding divisor (9) when remainder equals 0 is taken as HCF.

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