HCF of 2 and 8

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

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

What is HCF of 2 and 8?

Answer: HCF of 2 and 8 is 2.

Explanation:

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

Methods to Find HCF of 2 and 8

The methods to find the HCF of 2 and 8 are explained below.

Prime Factorization Method
Using Euclid's Algorithm
Listing Common Factors

HCF of 2 and 8 by Prime Factorization

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

HCF of 2 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.

Here X = 8 and Y = 2

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 and 8 is 2.

HCF of 2 and 8 by Listing Common Factors

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

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

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HCF of 2 and 8 Examples

Example 1: Find the HCF of 2 and 8, if their LCM is 8.

Solution:

∵ LCM × HCF = 2 × 8
⇒ HCF(2, 8) = (2 × 8)/8 = 2
Therefore, the highest common factor of 2 and 8 is 2.
Example 2: Find the highest number that divides 2 and 8 exactly.

Solution:

The highest number that divides 2 and 8 exactly is their highest common factor, i.e. HCF of 2 and 8.
⇒ Factors of 2 and 8:
- Factors of 2 = 1, 2
- Factors of 8 = 1, 2, 4, 8
Therefore, the HCF of 2 and 8 is 2.
Example 3: For two numbers, HCF = 2 and LCM = 8. If one number is 8, find the other number.

Solution:

Given: HCF (z, 8) = 2 and LCM (z, 8) = 8
∵ HCF × LCM = 8 × (z)
⇒ z = (HCF × LCM)/8
⇒ z = (2 × 8)/8
⇒ z = 2
Therefore, the other number is 2.

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FAQs on HCF of 2 and 8

What is the HCF of 2 and 8?

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

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

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 2 and 8, i.e. HCF × LCM = 2 × 8.

How to Find the HCF of 2 and 8 by Long Division Method?

To find the HCF of 2, 8 using long division method, 8 is divided by 2. The corresponding divisor (2) when remainder equals 0 is taken as HCF.

If the HCF of 8 and 2 is 2, Find its LCM.

HCF(8, 2) × LCM(8, 2) = 8 × 2
Since the HCF of 8 and 2 = 2
⇒ 2 × LCM(8, 2) = 16
Therefore, LCM = 8
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What are the Methods to Find HCF of 2 and 8?

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

By Prime Factorization
By Listing Common Factors
By Long Division

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

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