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HCF of 20, 28 and 36
HCF of 20, 28 and 36 is the largest possible number that divides 20, 28 and 36 exactly without any remainder. The factors of 20, 28 and 36 are (1, 2, 4, 5, 10, 20), (1, 2, 4, 7, 14, 28) and (1, 2, 3, 4, 6, 9, 12, 18, 36) respectively. There are 3 commonly used methods to find the HCF of 20, 28 and 36  Euclidean algorithm, prime factorization, and long division.
1.  HCF of 20, 28 and 36 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 20, 28 and 36?
Answer: HCF of 20, 28 and 36 is 4.
Explanation:
The HCF of three nonzero integers, x(20), y(28) and z(36), is the highest positive integer m(4) that divides x(20), y(28) and z(36) without any remainder.
Methods to Find HCF of 20, 28 and 36
The methods to find the HCF of 20, 28 and 36 are explained below.
 Listing Common Factors
 Prime Factorization Method
 Using Euclid's Algorithm
HCF of 20, 28 and 36 by Listing Common Factors
 Factors of 20: 1, 2, 4, 5, 10, 20
 Factors of 28: 1, 2, 4, 7, 14, 28
 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
There are 3 common factors of 20, 28 and 36, that are 1, 2, and 4. Therefore, the highest common factor of 20, 28 and 36 is 4.
HCF of 20, 28 and 36 by Prime Factorization
Prime factorization of 20, 28 and 36 is (2 × 2 × 5), (2 × 2 × 7) and (2 × 2 × 3 × 3) respectively. As visible, 20, 28 and 36 have common prime factors. Hence, the HCF of 20, 28 and 36 is 2 × 2 = 4.
HCF of 20, 28 and 36 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.
HCF(20, 28, 36) = HCF(HCF(20, 28), 36)
 HCF(28, 20) = HCF(20, 28 mod 20) = HCF(20, 8)
 HCF(20, 8) = HCF(8, 20 mod 8) = HCF(8, 4)
 HCF(8, 4) = HCF(4, 8 mod 4) = HCF(4, 0)
 HCF(4, 0) = 4 (∵ HCF(X, 0) = X, where X ≠ 0)
Steps for HCF(4, 36)
 HCF(36, 4) = HCF(4, 36 mod 4) = HCF(4, 0)
 HCF(4, 0) = 4 (∵ HCF(X, 0) = X, where X ≠ 0)
Therefore, the value of HCF of 20, 28 and 36 is 4.
☛ Also Check:
 HCF of 5 and 10 = 5
 HCF of 12 and 15 = 3
 HCF of 36 and 84 = 12
 HCF of 6 and 8 = 2
 HCF of 120 and 168 = 24
 HCF of 6, 8 and 12 = 2
 HCF of 441, 567 and 693 = 63
HCF of 20, 28 and 36 Examples

Example 1: Verify the relation between the LCM and HCF of 20, 28 and 36.
Solution:
The relation between the LCM and HCF of 20, 28 and 36 is given as, HCF(20, 28, 36) = [(20 × 28 × 36) × LCM(20, 28, 36)]/[LCM(20, 28) × LCM (28, 36) × LCM(20, 36)]
⇒ Prime factorization of 20, 28 and 36: 20 = 2 × 2 × 5
 28 = 2 × 2 × 7
 36 = 2 × 2 × 3 × 3
∴ LCM of (20, 28), (28, 36), (20, 36), and (20, 28, 36) is 140, 252, 180, and 1260 respectively.
Now, LHS = HCF(20, 28, 36) = 4.
And, RHS = [(20 × 28 × 36) × LCM(20, 28, 36)]/[LCM(20, 28) × LCM (28, 36) × LCM(20, 36)] = [(20160) × 1260]/[140 × 252 × 180]
LHS = RHS = 4.
Hence verified. 
Example 2: Calculate the HCF of 20, 28, and 36 using LCM of the given numbers.
Solution:
Prime factorization of 20, 28 and 36 is given as,
 20 = 2 × 2 × 5
 28 = 2 × 2 × 7
 36 = 2 × 2 × 3 × 3
LCM(20, 28) = 140, LCM(28, 36) = 252, LCM(36, 20) = 180, LCM(20, 28, 36) = 1260
⇒ HCF(20, 28, 36) = [(20 × 28 × 36) × LCM(20, 28, 36)]/[LCM(20, 28) × LCM (28, 36) × LCM(36, 20)]
⇒ HCF(20, 28, 36) = (20160 × 1260)/(140 × 252 × 180)
⇒ HCF(20, 28, 36) = 4.
Therefore, the HCF of 20, 28 and 36 is 4. 
Example 3: Find the highest number that divides 20, 28, and 36 completely.
Solution:
The highest number that divides 20, 28, and 36 exactly is their highest common factor.
 Factors of 20 = 1, 2, 4, 5, 10, 20
 Factors of 28 = 1, 2, 4, 7, 14, 28
 Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
The HCF of 20, 28, and 36 is 4.
∴ The highest number that divides 20, 28, and 36 is 4.
FAQs on HCF of 20, 28 and 36
What is the HCF of 20, 28 and 36?
The HCF of 20, 28 and 36 is 4. To calculate the HCF of 20, 28 and 36, we need to factor each number (factors of 20 = 1, 2, 4, 5, 10, 20; factors of 28 = 1, 2, 4, 7, 14, 28; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the highest factor that exactly divides 20, 28 and 36, i.e., 4.
What are the Methods to Find HCF of 20, 28 and 36?
There are three commonly used methods to find the HCF of 20, 28 and 36.
 By Long Division
 By Prime Factorization
 By Listing Common Factors
Which of the following is HCF of 20, 28 and 36? 4, 40, 76, 85, 80
HCF of 20, 28, 36 will be the number that divides 20, 28, and 36 without leaving any remainder. The only number that satisfies the given condition is 4.
What is the Relation Between LCM and HCF of 20, 28 and 36?
The following equation can be used to express the relation between Least Common Multiple and HCF of 20, 28 and 36, i.e. HCF(20, 28, 36) = [(20 × 28 × 36) × LCM(20, 28, 36)]/[LCM(20, 28) × LCM (28, 36) × LCM(20, 36)].
☛ Highest Common Factor Calculator
How to Find the HCF of 20, 28 and 36 by Prime Factorization?
To find the HCF of 20, 28 and 36, we will find the prime factorization of given numbers, i.e. 20 = 2 × 2 × 5; 28 = 2 × 2 × 7; 36 = 2 × 2 × 3 × 3.
⇒ Since 2, 2 are common terms in the prime factorization of 20, 28 and 36. Hence, HCF(20, 28, 36) = 2 × 2 = 4
☛ What is a Prime Number?
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