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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 non-zero 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 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.

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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)].
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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
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