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HCF of 4 and 8

HCF of 4 and 8 is the largest possible number that divides 4 and 8 exactly without any remainder. The factors of 4 and 8 are 1, 2, 4 and 1, 2, 4, 8 respectively. There are 3 commonly used methods to find the HCF of 4 and 8 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 4 and 8
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 4 and 8?

Answer: HCF of 4 and 8 is 4.

Explanation:

The HCF of two non-zero integers, x(4) and y(8), is the highest positive integer m(4) that divides both x(4) and y(8) without any remainder.

Methods to Find HCF of 4 and 8

Let's look at the different methods for finding the HCF of 4 and 8.

Prime Factorization Method
Using Euclid's Algorithm
Listing Common Factors

HCF of 4 and 8 by Prime Factorization

Prime factorization of 4 and 8 is (2 × 2) and (2 × 2 × 2) respectively. As visible, 4 and 8 have common prime factors. Hence, the HCF of 4 and 8 is 2 × 2 = 4.

HCF of 4 and 8 by Euclidean Algorithm

As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and the mod is the modulo operator.

Here X = 8 and Y = 4

HCF(8, 4) = HCF(4, 8 mod 4) = HCF(4, 0)
HCF(4, 0) = 4 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 4 and 8 is 4.

HCF of 4 and 8 by Listing Common Factors

Factors of 4: 1, 2, 4
Factors of 8: 1, 2, 4, 8

There are 3 common factors of 4 and 8, that are 1, 2, and 4. Therefore, the highest common factor of 4 and 8 is 4.

☛ Also Check:

HCF of 4 and 8 Examples

Example 1: Find the HCF of 4 and 8, if their LCM is 8.

Solution:

∵ LCM × HCF = 4 × 8
⇒ HCF(4, 8) = (4 × 8)/8 = 4
Therefore, the highest common factor of 4 and 8 is 4.
Example 2: For two numbers, HCF = 4 and LCM = 8. If one number is 4, find the other number.

Solution:

Given: HCF (z, 4) = 4 and LCM (z, 4) = 8
∵ HCF × LCM = 4 × (z)
⇒ z = (HCF × LCM)/4
⇒ z = (4 × 8)/4
⇒ z = 8
Therefore, the other number is 8.
Example 3: The product of two numbers is 32. If their HCF is 4, what is their LCM?

Solution:

Given: HCF = 4 and product of numbers = 32
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 32/4
Therefore, the LCM is 8.

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FAQs on HCF of 4 and 8

What is the HCF of 4 and 8?

The HCF of 4 and 8 is 4. To calculate the HCF of 4 and 8, we need to factor each number (factors of 4 = 1, 2, 4; factors of 8 = 1, 2, 4, 8) and choose the highest factor that exactly divides both 4 and 8, i.e., 4.

What are the Methods to Find HCF of 4 and 8?

There are three commonly used methods to find the HCF of 4 and 8.

By Listing Common Factors
By Prime Factorization
By Long Division

How to Find the HCF of 4 and 8 by Long Division Method?

To find the HCF of 4, 8 using long division method, 8 is divided by 4. The corresponding divisor (4) when remainder equals 0 is taken as HCF.

How to Find the HCF of 4 and 8 by Prime Factorization?

To find the HCF of 4 and 8, we will find the prime factorization of the given numbers, i.e. 4 = 2 × 2; 8 = 2 × 2 × 2.
⇒ Since 2, 2 are common terms in the prime factorization of 4 and 8. Hence, HCF(4, 8) = 2 × 2 = 4
☛ Prime Numbers

What is the Relation Between LCM and HCF of 4, 8?

The following equation can be used to express the relation between Least Common Multiple and HCF of 4 and 8, i.e. HCF × LCM = 4 × 8.

If the HCF of 8 and 4 is 4, Find its LCM.

HCF(8, 4) × LCM(8, 4) = 8 × 4
Since the HCF of 8 and 4 = 4
⇒ 4 × LCM(8, 4) = 32
Therefore, LCM = 8
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