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HCF of 2 and 6

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

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

What is HCF of 2 and 6?

Answer: HCF of 2 and 6 is 2.

Explanation:

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

Methods to Find HCF of 2 and 6

The methods to find the HCF of 2 and 6 are explained below.

Using Euclid's Algorithm
Listing Common Factors
Prime Factorization Method

HCF of 2 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.

Here X = 6 and Y = 2

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 and 6 is 2.

HCF of 2 and 6 by Listing Common Factors

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

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

HCF of 2 and 6 by Prime Factorization

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

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HCF of 2 and 6 Examples

Example 1: Find the highest number that divides 2 and 6 exactly.

Solution:

The highest number that divides 2 and 6 exactly is their highest common factor, i.e. HCF of 2 and 6.
⇒ Factors of 2 and 6:
- Factors of 2 = 1, 2
- Factors of 6 = 1, 2, 3, 6
Therefore, the HCF of 2 and 6 is 2.
Example 2: For two numbers, HCF = 2 and LCM = 6. If one number is 6, find the other number.

Solution:

Given: HCF (y, 6) = 2 and LCM (y, 6) = 6
∵ HCF × LCM = 6 × (y)
⇒ y = (HCF × LCM)/6
⇒ y = (2 × 6)/6
⇒ y = 2
Therefore, the other number is 2.
Example 3: The product of two numbers is 12. If their HCF is 2, what is their LCM?

Solution:

Given: HCF = 2 and product of numbers = 12
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 12/2
Therefore, the LCM is 6.

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FAQs on HCF of 2 and 6

What is the HCF of 2 and 6?

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

What is the Relation Between LCM and HCF of 2, 6?

The following equation can be used to express the relation between LCM and HCF of 2 and 6, i.e. HCF × LCM = 2 × 6.

How to Find the HCF of 2 and 6 by Prime Factorization?

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

What are the Methods to Find HCF of 2 and 6?

There are three commonly used methods to find the HCF of 2 and 6.

By Listing Common Factors
By Prime Factorization
By Long Division

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

HCF(6, 2) × LCM(6, 2) = 6 × 2
Since the HCF of 6 and 2 = 2
⇒ 2 × LCM(6, 2) = 12
Therefore, LCM = 6
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How to Find the HCF of 2 and 6 by Long Division Method?

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

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