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 nonzero 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 12, 45 and 75 = 3
 HCF of 306 and 657 = 9
 HCF of 64 and 72 = 8
 HCF of 24, 36 and 40 = 4
 HCF of 12, 24 and 36 = 12
 HCF of 2, 4 and 6 = 2
 HCF of 36, 42 and 48 = 6
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.
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