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HCF of 2, 4 and 8

HCF of 2, 4 and 8 is the largest possible number that divides 2, 4 and 8 exactly without any remainder. The factors of 2, 4 and 8 are (1, 2), (1, 2, 4) and (1, 2, 4, 8) respectively. There are 3 commonly used methods to find the HCF of 2, 4 and 8 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 2, 4 and 8
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 2, 4 and 8?

Answer: HCF of 2, 4 and 8 is 2.

Explanation:

The HCF of three non-zero integers, x(2), y(4) and z(8), is the highest positive integer m(2) that divides x(2), y(4) and z(8) without any remainder.

Methods to Find HCF of 2, 4 and 8

Let's look at the different methods for finding the HCF of 2, 4 and 8.

Listing Common Factors
Using Euclid's Algorithm
Prime Factorization Method

HCF of 2, 4 and 8 by Listing Common Factors

Factors of 2: 1, 2
Factors of 4: 1, 2, 4
Factors of 8: 1, 2, 4, 8

There are 2 common factors of 2, 4 and 8, that are 1 and 2. Therefore, the highest common factor of 2, 4 and 8 is 2.

HCF of 2, 4 and 8 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(2, 4, 8) = HCF(HCF(2, 4), 8)

HCF(4, 2) = HCF(2, 4 mod 2) = HCF(2, 0)
HCF(2, 0) = 2 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Steps for HCF(2, 8)

HCF(8, 2) = HCF(2, 8 mod 2) = HCF(2, 0)
HCF(2, 0) = 2 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 2, 4 and 8 is 2.

HCF of 2, 4 and 8 by Prime Factorization

Prime factorization of 2, 4 and 8 is (2), (2 × 2) and (2 × 2 × 2) respectively. As visible, 2, 4 and 8 have only one common prime factor i.e. 2. Hence, the HCF of 2, 4 and 8 is 2.

☛ Also Check:

HCF of 2, 4 and 8 Examples

Example 1: Find the highest number that divides 2, 4, and 8 completely.

Solution:

The highest number that divides 2, 4, and 8 exactly is their highest common factor.
- Factors of 2 = 1, 2
- Factors of 4 = 1, 2, 4
- Factors of 8 = 1, 2, 4, 8
The HCF of 2, 4, and 8 is 2.
∴ The highest number that divides 2, 4, and 8 is 2.
Example 2: Verify the relation between the LCM and HCF of 2, 4 and 8.

Solution:

The relation between the LCM and HCF of 2, 4 and 8 is given as, HCF(2, 4, 8) = [(2 × 4 × 8) × LCM(2, 4, 8)]/[LCM(2, 4) × LCM (4, 8) × LCM(2, 8)]
⇒ Prime factorization of 2, 4 and 8:
- 2 = 2
- 4 = 2 × 2
- 8 = 2 × 2 × 2
∴ LCM of (2, 4), (4, 8), (2, 8), and (2, 4, 8) is 4, 8, 8, and 8 respectively.
Now, LHS = HCF(2, 4, 8) = 2.
And, RHS = [(2 × 4 × 8) × LCM(2, 4, 8)]/[LCM(2, 4) × LCM (4, 8) × LCM(2, 8)] = [(64) × 8]/[4 × 8 × 8]
LHS = RHS = 2.
Hence verified.
Example 3: Calculate the HCF of 2, 4, and 8 using LCM of the given numbers.

Solution:

Prime factorization of 2, 4 and 8 is given as,
- 2 = 2
- 4 = 2 × 2
- 8 = 2 × 2 × 2
LCM(2, 4) = 4, LCM(4, 8) = 8, LCM(8, 2) = 8, LCM(2, 4, 8) = 8
⇒ HCF(2, 4, 8) = [(2 × 4 × 8) × LCM(2, 4, 8)]/[LCM(2, 4) × LCM (4, 8) × LCM(8, 2)]
⇒ HCF(2, 4, 8) = (64 × 8)/(4 × 8 × 8)
⇒ HCF(2, 4, 8) = 2.
Therefore, the HCF of 2, 4 and 8 is 2.

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FAQs on HCF of 2, 4 and 8

What is the HCF of 2, 4 and 8?

The HCF of 2, 4 and 8 is 2. To calculate the highest common factor of 2, 4 and 8, we need to factor each number (factors of 2 = 1, 2; factors of 4 = 1, 2, 4; factors of 8 = 1, 2, 4, 8) and choose the highest factor that exactly divides 2, 4 and 8, i.e., 2.

Which of the following is HCF of 2, 4 and 8? 2, 14, 52, 20, 43, 52, 29

HCF of 2, 4, 8 will be the number that divides 2, 4, and 8 without leaving any remainder. The only number that satisfies the given condition is 2.

How to Find the HCF of 2, 4 and 8 by Prime Factorization?

To find the HCF of 2, 4 and 8, we will find the prime factorization of given numbers, i.e. 2 = 2; 4 = 2 × 2; 8 = 2 × 2 × 2.
⇒ Since 2 is the only common prime factor of 2, 4 and 8. Hence, HCF(2, 4, 8) = 2.
☛ What is a Prime Number?

What is the Relation Between LCM and HCF of 2, 4 and 8?

The following equation can be used to express the relation between LCM and HCF of 2, 4 and 8, i.e. HCF(2, 4, 8) = [(2 × 4 × 8) × LCM(2, 4, 8)]/[LCM(2, 4) × LCM (4, 8) × LCM(2, 8)].
☛ HCF Calculator

What are the Methods to Find HCF of 2, 4 and 8?

There are three commonly used methods to find the HCF of 2, 4 and 8.

By Prime Factorization
By Long Division
By Euclidean Algorithm

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