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HCF of 398, 436 and 542

HCF of 398, 436 and 542 is the largest possible number that divides 398, 436 and 542 exactly without any remainder. The factors of 398, 436 and 542 are (1, 2, 199, 398), (1, 2, 4, 109, 218, 436) and (1, 2, 271, 542) respectively. There are 3 commonly used methods to find the HCF of 398, 436 and 542 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 398, 436 and 542
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 398, 436 and 542?

Answer: HCF of 398, 436 and 542 is 2.

Explanation:

The HCF of three non-zero integers, x(398), y(436) and z(542), is the highest positive integer m(2) that divides x(398), y(436) and z(542) without any remainder.

Methods to Find HCF of 398, 436 and 542

The methods to find the HCF of 398, 436 and 542 are explained below.

Prime Factorization Method
Listing Common Factors
Using Euclid's Algorithm

HCF of 398, 436 and 542 by Prime Factorization

Prime factorization of 398, 436 and 542 is (2 × 199), (2 × 2 × 109) and (2 × 271) respectively. As visible, 398, 436 and 542 have only one common prime factor i.e. 2. Hence, the HCF of 398, 436 and 542 is 2.

HCF of 398, 436 and 542 by Listing Common Factors

Factors of 398: 1, 2, 199, 398
Factors of 436: 1, 2, 4, 109, 218, 436
Factors of 542: 1, 2, 271, 542

There are 2 common factors of 398, 436 and 542, that are 1 and 2. Therefore, the highest common factor of 398, 436 and 542 is 2.

HCF of 398, 436 and 542 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.

HCF(398, 436, 542) = HCF(HCF(398, 436), 542)

HCF(436, 398) = HCF(398, 436 mod 398) = HCF(398, 38)
HCF(398, 38) = HCF(38, 398 mod 38) = HCF(38, 18)
HCF(38, 18) = HCF(18, 38 mod 18) = HCF(18, 2)
HCF(18, 2) = HCF(2, 18 mod 2) = HCF(2, 0)
HCF(2, 0) = 2 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Steps for HCF(2, 542)

HCF(542, 2) = HCF(2, 542 mod 2) = HCF(2, 0)
HCF(2, 0) = 2 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 398, 436 and 542 is 2.

☛ Also Check:

HCF of 398, 436 and 542 Examples

Example 1: Calculate the HCF of 398, 436, and 542 using LCM of the given numbers.

Solution:

Prime factorization of 398, 436 and 542 is given as,
- 398 = 2 × 199
- 436 = 2 × 2 × 109
- 542 = 2 × 271
LCM(398, 436) = 86764, LCM(436, 542) = 118156, LCM(542, 398) = 107858, LCM(398, 436, 542) = 23513044
⇒ HCF(398, 436, 542) = [(398 × 436 × 542) × LCM(398, 436, 542)]/[LCM(398, 436) × LCM (436, 542) × LCM(542, 398)]
⇒ HCF(398, 436, 542) = (94052176 × 23513044)/(86764 × 118156 × 107858)
⇒ HCF(398, 436, 542) = 2.
Therefore, the HCF of 398, 436 and 542 is 2.
Example 2: Verify the relation between the LCM and HCF of 398, 436 and 542.

Solution:

The relation between the LCM and HCF of 398, 436 and 542 is given as, HCF(398, 436, 542) = [(398 × 436 × 542) × LCM(398, 436, 542)]/[LCM(398, 436) × LCM (436, 542) × LCM(398, 542)]
⇒ Prime factorization of 398, 436 and 542:
- 398 = 2 × 199
- 436 = 2 × 2 × 109
- 542 = 2 × 271
∴ LCM of (398, 436), (436, 542), (398, 542), and (398, 436, 542) is 86764, 118156, 107858, and 23513044 respectively.
Now, LHS = HCF(398, 436, 542) = 2.
And, RHS = [(398 × 436 × 542) × LCM(398, 436, 542)]/[LCM(398, 436) × LCM (436, 542) × LCM(398, 542)] = [(94052176) × 23513044]/[86764 × 118156 × 107858]
LHS = RHS = 2.
Hence verified.
Example 3: Find the highest number that divides 398, 436, and 542 completely.

Solution:

The highest number that divides 398, 436, and 542 exactly is their highest common factor.
- Factors of 398 = 1, 2, 199, 398
- Factors of 436 = 1, 2, 4, 109, 218, 436
- Factors of 542 = 1, 2, 271, 542
The HCF of 398, 436, and 542 is 2.
∴ The highest number that divides 398, 436, and 542 is 2.

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FAQs on HCF of 398, 436 and 542

What is the HCF of 398, 436 and 542?

The HCF of 398, 436 and 542 is 2. To calculate the highest common factor of 398, 436 and 542, we need to factor each number (factors of 398 = 1, 2, 199, 398; factors of 436 = 1, 2, 4, 109, 218, 436; factors of 542 = 1, 2, 271, 542) and choose the highest factor that exactly divides 398, 436 and 542, i.e., 2.

What are the Methods to Find HCF of 398, 436 and 542?

There are three commonly used methods to find the HCF of 398, 436 and 542.

By Long Division
By Euclidean Algorithm
By Prime Factorization

Which of the following is HCF of 398, 436 and 542? 2, 549, 575, 563, 582

HCF of 398, 436, 542 will be the number that divides 398, 436, and 542 without leaving any remainder. The only number that satisfies the given condition is 2.

How to Find the HCF of 398, 436 and 542 by Prime Factorization?

To find the HCF of 398, 436 and 542, we will find the prime factorization of given numbers, i.e. 398 = 2 × 199; 436 = 2 × 2 × 109; 542 = 2 × 271.
⇒ Since 2 is the only common prime factor of 398, 436 and 542. Hence, HCF(398, 436, 542) = 2.
☛ Prime Number

What is the Relation Between LCM and HCF of 398, 436 and 542?

The following equation can be used to express the relation between LCM and HCF of 398, 436 and 542, i.e. HCF(398, 436, 542) = [(398 × 436 × 542) × LCM(398, 436, 542)]/[LCM(398, 436) × LCM (436, 542) × LCM(398, 542)].
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