HCF of 2, 4 and 6
HCF of 2, 4 and 6 is the largest possible number that divides 2, 4 and 6 exactly without any remainder. The factors of 2, 4 and 6 are (1, 2), (1, 2, 4) and (1, 2, 3, 6) respectively. There are 3 commonly used methods to find the HCF of 2, 4 and 6  prime factorization, long division, and Euclidean algorithm.
1.  HCF of 2, 4 and 6 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 2, 4 and 6?
Answer: HCF of 2, 4 and 6 is 2.
Explanation:
The HCF of three nonzero integers, x(2), y(4) and z(6), is the highest positive integer m(2) that divides x(2), y(4) and z(6) without any remainder.
Methods to Find HCF of 2, 4 and 6
The methods to find the HCF of 2, 4 and 6 are explained below.
 Listing Common Factors
 Using Euclid's Algorithm
 Prime Factorization Method
HCF of 2, 4 and 6 by Listing Common Factors
 Factors of 2: 1, 2
 Factors of 4: 1, 2, 4
 Factors of 6: 1, 2, 3, 6
There are 2 common factors of 2, 4 and 6, that are 1 and 2. Therefore, the highest common factor of 2, 4 and 6 is 2.
HCF of 2, 4 and 6 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, 6) = HCF(HCF(2, 4), 6)
 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, 6)
 HCF(6, 2) = HCF(2, 6 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 6 is 2.
HCF of 2, 4 and 6 by Prime Factorization
Prime factorization of 2, 4 and 6 is (2), (2 × 2) and (2 × 3) respectively. As visible, 2, 4 and 6 have only one common prime factor i.e. 2. Hence, the HCF of 2, 4 and 6 is 2.
☛ Also Check:
 HCF of 96 and 120 = 24
 HCF of 20, 28 and 36 = 4
 HCF of 6, 8 and 12 = 2
 HCF of 186 and 403 = 31
 HCF of 16 and 36 = 4
 HCF of 12, 16 and 28 = 4
 HCF of 5, 15 and 20 = 5
HCF of 2, 4 and 6 Examples

Example 1: Find the highest number that divides 2, 4, and 6 completely.
Solution:
The highest number that divides 2, 4, and 6 exactly is their highest common factor.
 Factors of 2 = 1, 2
 Factors of 4 = 1, 2, 4
 Factors of 6 = 1, 2, 3, 6
The HCF of 2, 4, and 6 is 2.
∴ The highest number that divides 2, 4, and 6 is 2. 
Example 2: Verify the relation between the LCM and HCF of 2, 4 and 6.
Solution:
The relation between the LCM and HCF of 2, 4 and 6 is given as, HCF(2, 4, 6) = [(2 × 4 × 6) × LCM(2, 4, 6)]/[LCM(2, 4) × LCM (4, 6) × LCM(2, 6)]
⇒ Prime factorization of 2, 4 and 6: 2 = 2
 4 = 2 × 2
 6 = 2 × 3
∴ LCM of (2, 4), (4, 6), (2, 6), and (2, 4, 6) is 4, 12, 6, and 12 respectively.
Now, LHS = HCF(2, 4, 6) = 2.
And, RHS = [(2 × 4 × 6) × LCM(2, 4, 6)]/[LCM(2, 4) × LCM (4, 6) × LCM(2, 6)] = [(48) × 12]/[4 × 12 × 6]
LHS = RHS = 2.
Hence verified. 
Example 3: Calculate the HCF of 2, 4, and 6 using LCM of the given numbers.
Solution:
Prime factorization of 2, 4 and 6 is given as,
 2 = 2
 4 = 2 × 2
 6 = 2 × 3
LCM(2, 4) = 4, LCM(4, 6) = 12, LCM(6, 2) = 6, LCM(2, 4, 6) = 12
⇒ HCF(2, 4, 6) = [(2 × 4 × 6) × LCM(2, 4, 6)]/[LCM(2, 4) × LCM (4, 6) × LCM(6, 2)]
⇒ HCF(2, 4, 6) = (48 × 12)/(4 × 12 × 6)
⇒ HCF(2, 4, 6) = 2.
Therefore, the HCF of 2, 4 and 6 is 2.
FAQs on HCF of 2, 4 and 6
What is the HCF of 2, 4 and 6?
The HCF of 2, 4 and 6 is 2. To calculate the highest common factor (HCF) of 2, 4 and 6, we need to factor each number (factors of 2 = 1, 2; factors of 4 = 1, 2, 4; factors of 6 = 1, 2, 3, 6) and choose the highest factor that exactly divides 2, 4 and 6, i.e., 2.
Which of the following is HCF of 2, 4 and 6? 2, 22, 44, 33, 30, 42
HCF of 2, 4, 6 will be the number that divides 2, 4, and 6 without leaving any remainder. The only number that satisfies the given condition is 2.
What are the Methods to Find HCF of 2, 4 and 6?
There are three commonly used methods to find the HCF of 2, 4 and 6.
 By Long Division
 By Euclidean Algorithm
 By Prime Factorization
How to Find the HCF of 2, 4 and 6 by Prime Factorization?
To find the HCF of 2, 4 and 6, we will find the prime factorization of given numbers, i.e. 2 = 2; 4 = 2 × 2; 6 = 2 × 3.
⇒ Since 2 is the only common prime factor of 2, 4 and 6. Hence, HCF(2, 4, 6) = 2.
☛ What is a Prime Number?
What is the Relation Between LCM and HCF of 2, 4 and 6?
The following equation can be used to express the relation between Least Common Multiple and HCF of 2, 4 and 6, i.e. HCF(2, 4, 6) = [(2 × 4 × 6) × LCM(2, 4, 6)]/[LCM(2, 4) × LCM (4, 6) × LCM(2, 6)].
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