HCF of 6 and 20
HCF of 6 and 20 is the largest possible number that divides 6 and 20 exactly without any remainder. The factors of 6 and 20 are 1, 2, 3, 6 and 1, 2, 4, 5, 10, 20 respectively. There are 3 commonly used methods to find the HCF of 6 and 20  long division, prime factorization, and Euclidean algorithm.
1.  HCF of 6 and 20 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 6 and 20?
Answer: HCF of 6 and 20 is 2.
Explanation:
The HCF of two nonzero integers, x(6) and y(20), is the highest positive integer m(2) that divides both x(6) and y(20) without any remainder.
Methods to Find HCF of 6 and 20
Let's look at the different methods for finding the HCF of 6 and 20.
 Prime Factorization Method
 Using Euclid's Algorithm
 Long Division Method
HCF of 6 and 20 by Prime Factorization
Prime factorization of 6 and 20 is (2 × 3) and (2 × 2 × 5) respectively. As visible, 6 and 20 have only one common prime factor i.e. 2. Hence, the HCF of 6 and 20 is 2.
HCF of 6 and 20 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 = 20 and Y = 6
 HCF(20, 6) = HCF(6, 20 mod 6) = HCF(6, 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 6 and 20 is 2.
HCF of 6 and 20 by Long Division
HCF of 6 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 6 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (6) by the remainder (2).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (2) is the HCF of 6 and 20.
☛ Also Check:
 HCF of 32 and 40 = 8
 HCF of 12, 16 and 24 = 4
 HCF of 186 and 403 = 31
 HCF of 324 and 144 = 36
 HCF of 72, 108 and 180 = 36
 HCF of 20 and 35 = 5
 HCF of 36 and 144 = 36
HCF of 6 and 20 Examples

Example 1: The product of two numbers is 120. If their HCF is 2, what is their LCM?
Solution:
Given: HCF = 2 and product of numbers = 120
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 120/2
Therefore, the LCM is 60. 
Example 2: Find the HCF of 6 and 20, if their LCM is 60.
Solution:
∵ LCM × HCF = 6 × 20
⇒ HCF(6, 20) = (6 × 20)/60 = 2
Therefore, the highest common factor of 6 and 20 is 2. 
Example 3: Find the highest number that divides 6 and 20 exactly.
Solution:
The highest number that divides 6 and 20 exactly is their highest common factor, i.e. HCF of 6 and 20.
⇒ Factors of 6 and 20: Factors of 6 = 1, 2, 3, 6
 Factors of 20 = 1, 2, 4, 5, 10, 20
Therefore, the HCF of 6 and 20 is 2.
FAQs on HCF of 6 and 20
What is the HCF of 6 and 20?
The HCF of 6 and 20 is 2. To calculate the Highest common factor of 6 and 20, we need to factor each number (factors of 6 = 1, 2, 3, 6; factors of 20 = 1, 2, 4, 5, 10, 20) and choose the highest factor that exactly divides both 6 and 20, i.e., 2.
What is the Relation Between LCM and HCF of 6, 20?
The following equation can be used to express the relation between LCM and HCF of 6 and 20, i.e. HCF × LCM = 6 × 20.
If the HCF of 20 and 6 is 2, Find its LCM.
HCF(20, 6) × LCM(20, 6) = 20 × 6
Since the HCF of 20 and 6 = 2
⇒ 2 × LCM(20, 6) = 120
Therefore, LCM = 60
☛ Highest Common Factor Calculator
What are the Methods to Find HCF of 6 and 20?
There are three commonly used methods to find the HCF of 6 and 20.
 By Prime Factorization
 By Listing Common Factors
 By Long Division
How to Find the HCF of 6 and 20 by Prime Factorization?
To find the HCF of 6 and 20, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 20 = 2 × 2 × 5.
⇒ Since 2 is the only common prime factor of 6 and 20. Hence, HCF (6, 20) = 2.
☛ What are Prime Numbers?
How to Find the HCF of 6 and 20 by Long Division Method?
To find the HCF of 6, 20 using long division method, 20 is divided by 6. The corresponding divisor (2) when remainder equals 0 is taken as HCF.
visual curriculum