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HCF of 391 and 667

HCF of 391 and 667 is the largest possible number that divides 391 and 667 exactly without any remainder. The factors of 391 and 667 are 1, 17, 23, 391 and 1, 23, 29, 667 respectively. There are 3 commonly used methods to find the HCF of 391 and 667 - long division, prime factorization, and Euclidean algorithm.

1.	HCF of 391 and 667
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 391 and 667?

Answer: HCF of 391 and 667 is 23.

Explanation:

The HCF of two non-zero integers, x(391) and y(667), is the highest positive integer m(23) that divides both x(391) and y(667) without any remainder.

Methods to Find HCF of 391 and 667

Let's look at the different methods for finding the HCF of 391 and 667.

Listing Common Factors
Long Division Method
Prime Factorization Method

HCF of 391 and 667 by Listing Common Factors

Factors of 391: 1, 17, 23, 391
Factors of 667: 1, 23, 29, 667

There are 2 common factors of 391 and 667, that are 1 and 23. Therefore, the highest common factor of 391 and 667 is 23.

HCF of 391 and 667 by Long Division

HCF of 391 and 667 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 667 (larger number) by 391 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (391) by the remainder (276).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (23) is the HCF of 391 and 667.

HCF of 391 and 667 by Prime Factorization

Prime factorization of 391 and 667 is (17 × 23) and (23 × 29) respectively. As visible, 391 and 667 have only one common prime factor i.e. 23. Hence, the HCF of 391 and 667 is 23.

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HCF of 391 and 667 Examples

Example 1: For two numbers, HCF = 23 and LCM = 11339. If one number is 667, find the other number.

Solution:

Given: HCF (y, 667) = 23 and LCM (y, 667) = 11339
∵ HCF × LCM = 667 × (y)
⇒ y = (HCF × LCM)/667
⇒ y = (23 × 11339)/667
⇒ y = 391
Therefore, the other number is 391.
Example 2: The product of two numbers is 260797. If their HCF is 23, what is their LCM?

Solution:

Given: HCF = 23 and product of numbers = 260797
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 260797/23
Therefore, the LCM is 11339.
Example 3: Find the highest number that divides 391 and 667 exactly.

Solution:

The highest number that divides 391 and 667 exactly is their highest common factor, i.e. HCF of 391 and 667.
⇒ Factors of 391 and 667:
- Factors of 391 = 1, 17, 23, 391
- Factors of 667 = 1, 23, 29, 667
Therefore, the HCF of 391 and 667 is 23.

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FAQs on HCF of 391 and 667

What is the HCF of 391 and 667?

The HCF of 391 and 667 is 23. To calculate the HCF (Highest Common Factor) of 391 and 667, we need to factor each number (factors of 391 = 1, 17, 23, 391; factors of 667 = 1, 23, 29, 667) and choose the highest factor that exactly divides both 391 and 667, i.e., 23.

What are the Methods to Find HCF of 391 and 667?

There are three commonly used methods to find the HCF of 391 and 667.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the HCF of 391 and 667 by Prime Factorization?

To find the HCF of 391 and 667, we will find the prime factorization of the given numbers, i.e. 391 = 17 × 23; 667 = 23 × 29.
⇒ Since 23 is the only common prime factor of 391 and 667. Hence, HCF (391, 667) = 23.
☛ What are Prime Numbers?

How to Find the HCF of 391 and 667 by Long Division Method?

To find the HCF of 391, 667 using long division method, 667 is divided by 391. The corresponding divisor (23) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 391, 667?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 391 and 667, i.e. HCF × LCM = 391 × 667.

If the HCF of 667 and 391 is 23, Find its LCM.

HCF(667, 391) × LCM(667, 391) = 667 × 391
Since the HCF of 667 and 391 = 23
⇒ 23 × LCM(667, 391) = 260797
Therefore, LCM = 11339
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