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HCF of 0 and 6

HCF of 0 and 6 would be the largest possible number that divides 0 and 6 exactly without any remainder. Factors of 0 and 6 are (1, 2, 3, 4, 5, 6, 7, . . .) and (1, 2, 3, 6) respectively. The different methods that can be used to calculate the HCF of 0 and 6 are- Euclid's algorithm and listing common factors.

1.	HCF of 0 and 6
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 0 and 6?

Answer: HCF of 0 and 6 is 6.

Explanation:

The HCF of two integers, x(0) and y(6), is the highest possible integer m(6) that divides both x(0) and y(6) without any remainder.

Methods to Find HCF of 0 and 6

The methods to find the HCF of 0 and 6 are explained below.

Using Euclid's Algorithm
Listing Common Factors

HCF of 0 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 = 0

∵ HCF(X, 0) = |X|, where X ≠ 0

⇒ HCF(6, 0) = 6

Therefore, the value of HCF of 0 and 6 is 6.

HCF of 0 and 6 by Listing Common Factors

Factors of 0: 1, 2, 3, 4, 5, 6, 7, . . .
[∵ 0/n = 0, ⇒ Every non-zero integer n is considered as a factor of 0.]
Factors of 6: 1, 2, 3, 6

6 is a number that divides both 0 and 6 completely without leaving any remainder. Therefore, the highest common factor of 0 and 6 is 6.

☛ Also Check:

HCF of 0 and 6 Examples

Example 1: Find the highest number that divides 0 and 6 exactly.

Solution:

The highest number that divides 0 and 6 exactly is their highest common factor, i.e. HCF of 0 and 6.
⇒ Factors of 0 and 6:

Factors of 0 = 1, 2, 3, 4, 5, 6, 7, . . .
[∵ 0/n = 0, ⇒ Every non-zero integer n is considered as a factor of 0.]
Factors of 6 = 1, 2, 3, 6
Therefore, the HCF of 0 and 6 is 6.
Example 2: Which of the following numbers is the HCF of 0 and 6?
a) 0 b) 1 c) 6 d) 3

Solution:

The HCF of 0 and 6 is the number that divides both 0 and 6 exactly without leaving any remainder. The only number that satisfies the given condition is 6.
Therefore, HCF(0, 6) = 6.

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FAQs on HCF of 0 and 6

What is the HCF of 0 and 6?

The HCF of 0 and 6 is 6. To calculate the HCF (Highest Common Factor) of 0 and 6, we need to factor each number (factors of 0 = 1, 2, 3, 4, 5, 6, . . .; factors of 6 = 1, 2, 3, 6) and choose the highest factor that exactly divides both 0 and 6, i.e., 6.

What are the Methods to Find HCF of 0 and 6?

There are two commonly used methods to find the HCF of 0 and 6.

By Listing Common Factors
By Euclidean Algorithm

How to Find the HCF of 0 and 6 by Listing Factors?

We know, 0/n = 0, where n ≠ 0 ⇒ Every non-zero integer n is considered as a factor of 0. ∴Factors of 0: 1, 2, 3, 4, 5, 6, 7, . . . Also, Factors of 6: 1, 2, 3, 6. Therefore, 6 divides both 0 and 6 without leaving any remainder. ⇒HCF(0, 6) = 6.

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