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HCF of 6 and 8

HCF of 6 and 8 is the largest possible number that divides 6 and 8 exactly without any remainder. The factors of 6 and 8 are 1, 2, 3, 6 and 1, 2, 4, 8 respectively. There are 3 commonly used methods to find the HCF of 6 and 8 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 6 and 8
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 6 and 8?

Answer: HCF of 6 and 8 is 2.

Explanation:

The HCF of two non-zero integers, x(6) and y(8), is the highest positive integer m(2) that divides both x(6) and y(8) without any remainder.

Methods to Find HCF of 6 and 8

Let's look at the different methods for finding the HCF of 6 and 8.

Long Division Method
Listing Common Factors
Prime Factorization Method

HCF of 6 and 8 by Long Division

HCF of 6 and 8 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 8 (larger number) by 6 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (6) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the HCF of 6 and 8.

HCF of 6 and 8 by Listing Common Factors

Factors of 6: 1, 2, 3, 6
Factors of 8: 1, 2, 4, 8

There are 2 common factors of 6 and 8, that are 1 and 2. Therefore, the highest common factor of 6 and 8 is 2.

HCF of 6 and 8 by Prime Factorization

Prime factorization of 6 and 8 is (2 × 3) and (2 × 2 × 2) respectively. As visible, 6 and 8 have only one common prime factor i.e. 2. Hence, the HCF of 6 and 8 is 2.

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HCF of 6 and 8 Examples

Example 1: For two numbers, HCF = 2 and LCM = 24. If one number is 6, find the other number.

Solution:

Given: HCF (y, 6) = 2 and LCM (y, 6) = 24
∵ HCF × LCM = 6 × (y)
⇒ y = (HCF × LCM)/6
⇒ y = (2 × 24)/6
⇒ y = 8
Therefore, the other number is 8.
Example 2: Find the HCF of 6 and 8, if their LCM is 24.

Solution:

∵ LCM × HCF = 6 × 8
⇒ HCF(6, 8) = (6 × 8)/24 = 2
Therefore, the highest common factor of 6 and 8 is 2.
Example 3: Find the highest number that divides 6 and 8 exactly.

Solution:

The highest number that divides 6 and 8 exactly is their highest common factor, i.e. HCF of 6 and 8.
⇒ Factors of 6 and 8:
- Factors of 6 = 1, 2, 3, 6
- Factors of 8 = 1, 2, 4, 8
Therefore, the HCF of 6 and 8 is 2.

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FAQs on HCF of 6 and 8

What is the HCF of 6 and 8?

The HCF of 6 and 8 is 2. To calculate the Highest common factor of 6 and 8, we need to factor each number (factors of 6 = 1, 2, 3, 6; factors of 8 = 1, 2, 4, 8) and choose the highest factor that exactly divides both 6 and 8, i.e., 2.

How to Find the HCF of 6 and 8 by Prime Factorization?

To find the HCF of 6 and 8, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 8 = 2 × 2 × 2.
⇒ Since 2 is the only common prime factor of 6 and 8. Hence, HCF (6, 8) = 2.
☛ What is a Prime Number?

What are the Methods to Find HCF of 6 and 8?

There are three commonly used methods to find the HCF of 6 and 8.

By Long Division
By Euclidean Algorithm
By Prime Factorization

If the HCF of 8 and 6 is 2, Find its LCM.

HCF(8, 6) × LCM(8, 6) = 8 × 6
Since the HCF of 8 and 6 = 2
⇒ 2 × LCM(8, 6) = 48
Therefore, LCM = 24
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What is the Relation Between LCM and HCF of 6, 8?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 6 and 8, i.e. HCF × LCM = 6 × 8.

How to Find the HCF of 6 and 8 by Long Division Method?

To find the HCF of 6, 8 using long division method, 8 is divided by 6. The corresponding divisor (2) when remainder equals 0 is taken as HCF.

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