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 nonzero 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 20, 30 and 40 = 10
 HCF of 64 and 72 = 8
 HCF of 12 and 36 = 12
 HCF of 84 and 144 = 12
 HCF of 408 and 1032 = 24
 HCF of 2 and 4 = 2
 HCF of 8 and 15 = 1
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.
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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