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HCF of 20, 25 and 30

HCF of 20, 25 and 30 is the largest possible number that divides 20, 25 and 30 exactly without any remainder. The factors of 20, 25 and 30 are (1, 2, 4, 5, 10, 20), (1, 5, 25) and (1, 2, 3, 5, 6, 10, 15, 30) respectively. There are 3 commonly used methods to find the HCF of 20, 25 and 30 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 20, 25 and 30
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 20, 25 and 30?

Answer: HCF of 20, 25 and 30 is 5.

Explanation:

The HCF of three non-zero integers, x(20), y(25) and z(30), is the highest positive integer m(5) that divides x(20), y(25) and z(30) without any remainder.

Methods to Find HCF of 20, 25 and 30

The methods to find the HCF of 20, 25 and 30 are explained below.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

HCF of 20, 25 and 30 by Long Division

HCF of 20, 25 and 30 can be represented as HCF of (HCF of 20, 25) and 30. HCF(20, 25, 30) can be thus calculated by first finding HCF(20, 25) using long division and thereafter using this result with 30 to perform long division again.

Step 1: Divide 25 (larger number) by 20 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (20) by the remainder (5). Repeat this process until the remainder = 0.
⇒ HCF(20, 25) = 5.
Step 3: Now to find the HCF of 5 and 30, we will perform a long division on 30 and 5.
Step 4: For remainder = 0, divisor = 5 ⇒ HCF(5, 30) = 5

Thus, HCF(20, 25, 30) = HCF(HCF(20, 25), 30) = 5.

HCF of 20, 25 and 30 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, 25, 30) = HCF(HCF(20, 25), 30)

HCF(25, 20) = HCF(20, 25 mod 20) = HCF(20, 5)
HCF(20, 5) = HCF(5, 20 mod 5) = HCF(5, 0)
HCF(5, 0) = 5 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Steps for HCF(5, 30)

HCF(30, 5) = HCF(5, 30 mod 5) = HCF(5, 0)
HCF(5, 0) = 5 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 20, 25 and 30 is 5.

HCF of 20, 25 and 30 by Listing Common Factors

Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 25: 1, 5, 25
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

There are 2 common factors of 20, 25 and 30, that are 1 and 5. Therefore, the highest common factor of 20, 25 and 30 is 5.

☛ Also Check:

HCF of 20, 25 and 30 Examples

Example 1: Find the highest number that divides 20, 25, and 30 completely.

Solution:

The highest number that divides 20, 25, and 30 exactly is their highest common factor.
- Factors of 20 = 1, 2, 4, 5, 10, 20
- Factors of 25 = 1, 5, 25
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
The HCF of 20, 25, and 30 is 5.
∴ The highest number that divides 20, 25, and 30 is 5.
Example 2: Calculate the HCF of 20, 25, and 30 using LCM of the given numbers.

Solution:

Prime factorization of 20, 25 and 30 is given as,
- 20 = 2 × 2 × 5
- 25 = 5 × 5
- 30 = 2 × 3 × 5
LCM(20, 25) = 100, LCM(25, 30) = 150, LCM(30, 20) = 60, LCM(20, 25, 30) = 300
⇒ HCF(20, 25, 30) = [(20 × 25 × 30) × LCM(20, 25, 30)]/[LCM(20, 25) × LCM (25, 30) × LCM(30, 20)]
⇒ HCF(20, 25, 30) = (15000 × 300)/(100 × 150 × 60)
⇒ HCF(20, 25, 30) = 5.
Therefore, the HCF of 20, 25 and 30 is 5.
Example 3: Verify the relation between the LCM and HCF of 20, 25 and 30.

Solution:

The relation between the LCM and HCF of 20, 25 and 30 is given as, HCF(20, 25, 30) = [(20 × 25 × 30) × LCM(20, 25, 30)]/[LCM(20, 25) × LCM (25, 30) × LCM(20, 30)]
⇒ Prime factorization of 20, 25 and 30:
- 20 = 2 × 2 × 5
- 25 = 5 × 5
- 30 = 2 × 3 × 5
∴ LCM of (20, 25), (25, 30), (20, 30), and (20, 25, 30) is 100, 150, 60, and 300 respectively.
Now, LHS = HCF(20, 25, 30) = 5.
And, RHS = [(20 × 25 × 30) × LCM(20, 25, 30)]/[LCM(20, 25) × LCM (25, 30) × LCM(20, 30)] = [(15000) × 300]/[100 × 150 × 60]
LHS = RHS = 5.
Hence verified.

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FAQs on HCF of 20, 25 and 30

What is the HCF of 20, 25 and 30?

The HCF of 20, 25 and 30 is 5. To calculate the HCF (Highest Common Factor) of 20, 25 and 30, we need to factor each number (factors of 20 = 1, 2, 4, 5, 10, 20; factors of 25 = 1, 5, 25; factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30) and choose the highest factor that exactly divides 20, 25 and 30, i.e., 5.

How to Find the HCF of 20, 25 and 30 by Prime Factorization?

To find the HCF of 20, 25 and 30, we will find the prime factorization of given numbers, i.e. 20 = 2 × 2 × 5; 25 = 5 × 5; 30 = 2 × 3 × 5.
⇒ Since 5 is the only common prime factor of 20, 25 and 30. Hence, HCF(20, 25, 30) = 5.
☛ Prime Number

What is the Relation Between LCM and HCF of 20, 25 and 30?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 20, 25 and 30, i.e. HCF(20, 25, 30) = [(20 × 25 × 30) × LCM(20, 25, 30)]/[LCM(20, 25) × LCM (25, 30) × LCM(20, 30)].
☛ HCF Calculator

Which of the following is HCF of 20, 25 and 30? 5, 48, 49, 68, 78, 67, 67, 43, 51

HCF of 20, 25, 30 will be the number that divides 20, 25, and 30 without leaving any remainder. The only number that satisfies the given condition is 5.

What are the Methods to Find HCF of 20, 25 and 30?

There are three commonly used methods to find the HCF of 20, 25 and 30.

By Long Division
By Euclidean Algorithm
By Prime Factorization

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