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HCF of 15, 25 and 30

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

1.	HCF of 15, 25 and 30
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 15, 25 and 30?

Answer: HCF of 15, 25 and 30 is 5.

Explanation:

The HCF of three non-zero integers, x(15), y(25) and z(30), is the highest positive integer m(5) that divides x(15), y(25) and z(30) without any remainder.

Methods to Find HCF of 15, 25 and 30

The methods to find the HCF of 15, 25 and 30 are explained below.

Listing Common Factors
Prime Factorization Method
Using Euclid's Algorithm

HCF of 15, 25 and 30 by Listing Common Factors

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

There are 2 common factors of 15, 25 and 30, that are 1 and 5. Therefore, the highest common factor of 15, 25 and 30 is 5.

HCF of 15, 25 and 30 by Prime Factorization

Prime factorization of 15, 25 and 30 is (3 × 5), (5 × 5) and (2 × 3 × 5) respectively. As visible, 15, 25 and 30 have only one common prime factor i.e. 5. Hence, the HCF of 15, 25 and 30 is 5.

HCF of 15, 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(15, 25, 30) = HCF(HCF(15, 25), 30)

HCF(25, 15) = HCF(15, 25 mod 15) = HCF(15, 10)
HCF(15, 10) = HCF(10, 15 mod 10) = HCF(10, 5)
HCF(10, 5) = HCF(5, 10 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 15, 25 and 30 is 5.

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HCF of 15, 25 and 30 Examples

Example 1: Calculate the HCF of 15, 25, and 30 using LCM of the given numbers.

Solution:

Prime factorization of 15, 25 and 30 is given as,
- 15 = 3 × 5
- 25 = 5 × 5
- 30 = 2 × 3 × 5
LCM(15, 25) = 75, LCM(25, 30) = 150, LCM(30, 15) = 30, LCM(15, 25, 30) = 150
⇒ HCF(15, 25, 30) = [(15 × 25 × 30) × LCM(15, 25, 30)]/[LCM(15, 25) × LCM (25, 30) × LCM(30, 15)]
⇒ HCF(15, 25, 30) = (11250 × 150)/(75 × 150 × 30)
⇒ HCF(15, 25, 30) = 5.
Therefore, the HCF of 15, 25 and 30 is 5.
Example 2: Verify the relation between the LCM and HCF of 15, 25 and 30.

Solution:

The relation between the LCM and HCF of 15, 25 and 30 is given as, HCF(15, 25, 30) = [(15 × 25 × 30) × LCM(15, 25, 30)]/[LCM(15, 25) × LCM (25, 30) × LCM(15, 30)]
⇒ Prime factorization of 15, 25 and 30:
- 15 = 3 × 5
- 25 = 5 × 5
- 30 = 2 × 3 × 5
∴ LCM of (15, 25), (25, 30), (15, 30), and (15, 25, 30) is 75, 150, 30, and 150 respectively.
Now, LHS = HCF(15, 25, 30) = 5.
And, RHS = [(15 × 25 × 30) × LCM(15, 25, 30)]/[LCM(15, 25) × LCM (25, 30) × LCM(15, 30)] = [(11250) × 150]/[75 × 150 × 30]
LHS = RHS = 5.
Hence verified.
Example 3: Find the highest number that divides 15, 25, and 30 completely.

Solution:

The highest number that divides 15, 25, and 30 exactly is their highest common factor.
- Factors of 15 = 1, 3, 5, 15
- Factors of 25 = 1, 5, 25
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
The HCF of 15, 25, and 30 is 5.
∴ The highest number that divides 15, 25, and 30 is 5.

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FAQs on HCF of 15, 25 and 30

What is the HCF of 15, 25 and 30?

The HCF of 15, 25 and 30 is 5. To calculate the highest common factor (HCF) of 15, 25 and 30, we need to factor each number (factors of 15 = 1, 3, 5, 15; 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 15, 25 and 30, i.e., 5.

Which of the following is HCF of 15, 25 and 30? 5, 39, 57, 77, 50, 68

HCF of 15, 25, 30 will be the number that divides 15, 25, and 30 without leaving any remainder. The only number that satisfies the given condition is 5.

What is the Relation Between LCM and HCF of 15, 25 and 30?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 15, 25 and 30, i.e. HCF(15, 25, 30) = [(15 × 25 × 30) × LCM(15, 25, 30)]/[LCM(15, 25) × LCM (25, 30) × LCM(15, 30)].
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How to Find the HCF of 15, 25 and 30 by Prime Factorization?

To find the HCF of 15, 25 and 30, we will find the prime factorization of given numbers, i.e. 15 = 3 × 5; 25 = 5 × 5; 30 = 2 × 3 × 5.
⇒ Since 5 is the only common prime factor of 15, 25 and 30. Hence, HCF(15, 25, 30) = 5.
☛ What are Prime Numbers?

What are the Methods to Find HCF of 15, 25 and 30?

There are three commonly used methods to find the HCF of 15, 25 and 30.

By Long Division
By Prime Factorization
By Euclidean Algorithm

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