HCF of 391 and 667

The HCF of 391 and 667 is 23. The listing of common factors, prime factorisation and long division are the three most frequent methods for calculating the HCF of 391 and 667. The greatest number that divides 391 and 667 perfectly without leaving a remainder is called the HCF of these numbers. 1, 17, 23, 391 and 1, 23, 29, 667, respectively, are the factors of 391 and 667.

Also read: Highest common factor

What is the HCF of 391 and 667?

The answer to this question is 23. This article shows how to find the HCF of 391 and 667 using various methods for your reference. The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers.

How to Find HCF of 391 and 667?

There are three methods to find the HCF of 391 and 667:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 391 and 667 by Prime Factorisation Method

The prime factorisation of 391 and 667 is given by:

Prime factorisation of 391 = (17 × 23)

Prime factorisation of 667 = (23 × 29)

Hence, the HCF of 391 and 667 is 23.

HCF (391, 667) = 23

HCF of 391 and 667 by Long Division Method

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

HCF of 391 and 667

No further division can be done. 

Hence, HCF (391, 667) = 23

HCF of 391 and 667 by Listing Common Factors

To calculate the HCF of 391 and 667 by listing common factors, list the factors as shown below:

Factors of 391: 1, 17, 23, 391

Factors of 667: 1, 23, 29, 667

There are 2 common factors of 391 and 667, which are 1 and 23. Therefore, the Highest Common Factor of 391 and 667 is 23.

Related Articles

Video Lesson on Properties of HCF and LCM

HCF of 391 and 667 Solved Example

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.

Frequently Asked Questions on HCF of 391 and 667

Q1

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 and choose the highest factor that exactly divides both 391 and 667, .i.e 23.
Q2

How to find the HCF of 391 and 667 by prime factorisation?

To find the HCF of 391 and 667, we need to find the prime factorisation of the given numbers, .i.e 391 = 17 × 23; 667 = 23 × 29.
⇒ 23 is the only common prime factor of 391 and 667. Hence, HCF (391, 667) = 23.
Q3

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. They are:
Long Division
Listing Common Factors
Prime Factorisation
Q4

How to find the HCF of 391 and 667 by long division method?

To find the HCF of 391 and 667 using the long division method, 667 is divided by 391. The corresponding divisor (23), when remainder is 0, is the HCF.
Q5

What is the relation between LCM and HCF of 391 and 667?

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

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