HCF of 5 and 30

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

1.	HCF of 5 and 30
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 5 and 30?

Answer: HCF of 5 and 30 is 5.

Explanation:

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

Methods to Find HCF of 5 and 30

Let's look at the different methods for finding the HCF of 5 and 30.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

HCF of 5 and 30 by Long Division

HCF of 5 and 30 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 30 (larger number) by 5 (smaller number).
Step 2: Since the remainder = 0, the divisor (5) is the HCF of 5 and 30.

The corresponding divisor (5) is the HCF of 5 and 30.

HCF of 5 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.

Here X = 30 and Y = 5

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 5 and 30 is 5.

HCF of 5 and 30 by Listing Common Factors

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

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

☛ Also Check:

HCF of 5 and 30 Examples

Example 1: The product of two numbers is 150. If their HCF is 5, what is their LCM?

Solution:

Given: HCF = 5 and product of numbers = 150
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 150/5
Therefore, the LCM is 30.
Example 2: Find the highest number that divides 5 and 30 exactly.

Solution:

The highest number that divides 5 and 30 exactly is their highest common factor, i.e. HCF of 5 and 30.
⇒ Factors of 5 and 30:
- Factors of 5 = 1, 5
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Therefore, the HCF of 5 and 30 is 5.
Example 3: For two numbers, HCF = 5 and LCM = 30. If one number is 30, find the other number.

Solution:

Given: HCF (y, 30) = 5 and LCM (y, 30) = 30
∵ HCF × LCM = 30 × (y)
⇒ y = (HCF × LCM)/30
⇒ y = (5 × 30)/30
⇒ y = 5
Therefore, the other number is 5.

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FAQs on HCF of 5 and 30

What is the HCF of 5 and 30?

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

What is the Relation Between LCM and HCF of 5, 30?

The following equation can be used to express the relation between Least Common Multiple and HCF of 5 and 30, i.e. HCF × LCM = 5 × 30.

How to Find the HCF of 5 and 30 by Prime Factorization?

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

If the HCF of 30 and 5 is 5, Find its LCM.

HCF(30, 5) × LCM(30, 5) = 30 × 5
Since the HCF of 30 and 5 = 5
⇒ 5 × LCM(30, 5) = 150
Therefore, LCM = 30
☛ Highest Common Factor Calculator

How to Find the HCF of 5 and 30 by Long Division Method?

To find the HCF of 5, 30 using long division method, 30 is divided by 5. The corresponding divisor (5) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 5 and 30?

There are three commonly used methods to find the HCF of 5 and 30.

By Prime Factorization
By Long Division
By Euclidean Algorithm

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