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 nonzero 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.
☛ Also Check:
 HCF of 12 and 20 = 4
 HCF of 9 and 12 = 3
 HCF of 34 and 102 = 34
 HCF of 65 and 117 = 13
 HCF of 40 and 80 = 40
 HCF of 16 and 27 = 1
 HCF of 8, 9 and 25 = 1
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.
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
☛ HCF Calculator
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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