HCF of 8 and 20
HCF of 8 and 20 is the largest possible number that divides 8 and 20 exactly without any remainder. The factors of 8 and 20 are 1, 2, 4, 8 and 1, 2, 4, 5, 10, 20 respectively. There are 3 commonly used methods to find the HCF of 8 and 20  Euclidean algorithm, long division, and prime factorization.
1.  HCF of 8 and 20 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 8 and 20?
Answer: HCF of 8 and 20 is 4.
Explanation:
The HCF of two nonzero integers, x(8) and y(20), is the highest positive integer m(4) that divides both x(8) and y(20) without any remainder.
Methods to Find HCF of 8 and 20
Let's look at the different methods for finding the HCF of 8 and 20.
 Long Division Method
 Listing Common Factors
 Prime Factorization Method
HCF of 8 and 20 by Long Division
HCF of 8 and 20 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 20 (larger number) by 8 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (8) by the remainder (4).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (4) is the HCF of 8 and 20.
HCF of 8 and 20 by Listing Common Factors
 Factors of 8: 1, 2, 4, 8
 Factors of 20: 1, 2, 4, 5, 10, 20
There are 3 common factors of 8 and 20, that are 1, 2, and 4. Therefore, the highest common factor of 8 and 20 is 4.
HCF of 8 and 20 by Prime Factorization
Prime factorization of 8 and 20 is (2 × 2 × 2) and (2 × 2 × 5) respectively. As visible, 8 and 20 have common prime factors. Hence, the HCF of 8 and 20 is 2 × 2 = 4.
☛ Also Check:
 HCF of 12 and 30 = 6
 HCF of 84 and 98 = 14
 HCF of 144, 180 and 192 = 12
 HCF of 14 and 21 = 7
 HCF of 34 and 85 = 17
 HCF of 1001 and 910 = 91
 HCF of 1152 and 1664 = 128
HCF of 8 and 20 Examples

Example 1: Find the HCF of 8 and 20, if their LCM is 40.
Solution:
∵ LCM × HCF = 8 × 20
⇒ HCF(8, 20) = (8 × 20)/40 = 4
Therefore, the highest common factor of 8 and 20 is 4. 
Example 2: The product of two numbers is 160. If their HCF is 4, what is their LCM?
Solution:
Given: HCF = 4 and product of numbers = 160
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 160/4
Therefore, the LCM is 40. 
Example 3: For two numbers, HCF = 4 and LCM = 40. If one number is 20, find the other number.
Solution:
Given: HCF (x, 20) = 4 and LCM (x, 20) = 40
∵ HCF × LCM = 20 × (x)
⇒ x = (HCF × LCM)/20
⇒ x = (4 × 40)/20
⇒ x = 8
Therefore, the other number is 8.
FAQs on HCF of 8 and 20
What is the HCF of 8 and 20?
The HCF of 8 and 20 is 4. To calculate the Highest common factor of 8 and 20, we need to factor each number (factors of 8 = 1, 2, 4, 8; factors of 20 = 1, 2, 4, 5, 10, 20) and choose the highest factor that exactly divides both 8 and 20, i.e., 4.
What are the Methods to Find HCF of 8 and 20?
There are three commonly used methods to find the HCF of 8 and 20.
 By Prime Factorization
 By Euclidean Algorithm
 By Long Division
If the HCF of 20 and 8 is 4, Find its LCM.
HCF(20, 8) × LCM(20, 8) = 20 × 8
Since the HCF of 20 and 8 = 4
⇒ 4 × LCM(20, 8) = 160
Therefore, LCM = 40
☛ HCF Calculator
What is the Relation Between LCM and HCF of 8, 20?
The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 8 and 20, i.e. HCF × LCM = 8 × 20.
How to Find the HCF of 8 and 20 by Prime Factorization?
To find the HCF of 8 and 20, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 20 = 2 × 2 × 5.
⇒ Since 2, 2 are common terms in the prime factorization of 8 and 20. Hence, HCF(8, 20) = 2 × 2 = 4
☛ Prime Numbers
How to Find the HCF of 8 and 20 by Long Division Method?
To find the HCF of 8, 20 using long division method, 20 is divided by 8. The corresponding divisor (4) when remainder equals 0 is taken as HCF.
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