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HCF of 399 and 437

HCF of 399 and 437 is the largest possible number that divides 399 and 437 exactly without any remainder. The factors of 399 and 437 are 1, 3, 7, 19, 21, 57, 133, 399 and 1, 19, 23, 437 respectively. There are 3 commonly used methods to find the HCF of 399 and 437 - long division, prime factorization, and Euclidean algorithm.

1.	HCF of 399 and 437
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 399 and 437?

Answer: HCF of 399 and 437 is 19.

Explanation:

The HCF of two non-zero integers, x(399) and y(437), is the highest positive integer m(19) that divides both x(399) and y(437) without any remainder.

Methods to Find HCF of 399 and 437

The methods to find the HCF of 399 and 437 are explained below.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

HCF of 399 and 437 by Long Division

HCF of 399 and 437 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 437 (larger number) by 399 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (399) by the remainder (38).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (19) is the HCF of 399 and 437.

HCF of 399 and 437 by Prime Factorization

Prime factorization of 399 and 437 is (3 × 7 × 19) and (19 × 23) respectively. As visible, 399 and 437 have only one common prime factor i.e. 19. Hence, the HCF of 399 and 437 is 19.

HCF of 399 and 437 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 = 437 and Y = 399

HCF(437, 399) = HCF(399, 437 mod 399) = HCF(399, 38)
HCF(399, 38) = HCF(38, 399 mod 38) = HCF(38, 19)
HCF(38, 19) = HCF(19, 38 mod 19) = HCF(19, 0)
HCF(19, 0) = 19 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 399 and 437 is 19.

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HCF of 399 and 437 Examples

Example 1: Find the highest number that divides 399 and 437 exactly.

Solution:

The highest number that divides 399 and 437 exactly is their highest common factor, i.e. HCF of 399 and 437.
⇒ Factors of 399 and 437:
- Factors of 399 = 1, 3, 7, 19, 21, 57, 133, 399
- Factors of 437 = 1, 19, 23, 437
Therefore, the HCF of 399 and 437 is 19.
Example 2: Find the HCF of 399 and 437, if their LCM is 9177.

Solution:

∵ LCM × HCF = 399 × 437
⇒ HCF(399, 437) = (399 × 437)/9177 = 19
Therefore, the highest common factor of 399 and 437 is 19.
Example 3: The product of two numbers is 174363. If their HCF is 19, what is their LCM?

Solution:

Given: HCF = 19 and product of numbers = 174363
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 174363/19
Therefore, the LCM is 9177.

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FAQs on HCF of 399 and 437

What is the HCF of 399 and 437?

The HCF of 399 and 437 is 19. To calculate the HCF (Highest Common Factor) of 399 and 437, we need to factor each number (factors of 399 = 1, 3, 7, 19, 21, 57, 133, 399; factors of 437 = 1, 19, 23, 437) and choose the highest factor that exactly divides both 399 and 437, i.e., 19.

How to Find the HCF of 399 and 437 by Prime Factorization?

To find the HCF of 399 and 437, we will find the prime factorization of the given numbers, i.e. 399 = 3 × 7 × 19; 437 = 19 × 23.
⇒ Since 19 is the only common prime factor of 399 and 437. Hence, HCF (399, 437) = 19.
☛ Prime Number

How to Find the HCF of 399 and 437 by Long Division Method?

To find the HCF of 399, 437 using long division method, 437 is divided by 399. The corresponding divisor (19) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 399, 437?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 399 and 437, i.e. HCF × LCM = 399 × 437.

If the HCF of 437 and 399 is 19, Find its LCM.

HCF(437, 399) × LCM(437, 399) = 437 × 399
Since the HCF of 437 and 399 = 19
⇒ 19 × LCM(437, 399) = 174363
Therefore, LCM = 9177
☛ Highest Common Factor Calculator

What are the Methods to Find HCF of 399 and 437?

There are three commonly used methods to find the HCF of 399 and 437.

By Prime Factorization
By Euclidean Algorithm
By Long Division

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