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 nonzero 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.
☛ Also Check:
 HCF of 324 and 144 = 36
 HCF of 3 and 7 = 1
 HCF of 120, 144 and 204 = 12
 HCF of 10 and 12 = 2
 HCF of 16 and 24 = 8
 HCF of 6 and 10 = 2
 HCF of 60 and 75 = 15
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.
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
☛ HCF Calculator
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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