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HCF of 20 and 30

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

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

What is HCF of 20 and 30?

Answer: HCF of 20 and 30 is 10.

Explanation:

The HCF of two non-zero integers, x(20) and y(30), is the highest positive integer m(10) that divides both x(20) and y(30) without any remainder.

Methods to Find HCF of 20 and 30

Let's look at the different methods for finding the HCF of 20 and 30.

Long Division Method
Listing Common Factors
Prime Factorization Method

HCF of 20 and 30 by Long Division

HCF of 20 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 20 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (20) by the remainder (10).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (10) is the HCF of 20 and 30.

HCF of 20 and 30 by Listing Common Factors

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

There are 4 common factors of 20 and 30, that are 1, 2, 10, and 5. Therefore, the highest common factor of 20 and 30 is 10.

HCF of 20 and 30 by Prime Factorization

Prime factorization of 20 and 30 is (2 × 2 × 5) and (2 × 3 × 5) respectively. As visible, 20 and 30 have common prime factors. Hence, the HCF of 20 and 30 is 2 × 5 = 10.

☛ Also Check:

HCF of 20 and 30 Examples

Example 1: Find the HCF of 20 and 30, if their LCM is 60.

Solution:

∵ LCM × HCF = 20 × 30
⇒ HCF(20, 30) = (20 × 30)/60 = 10
Therefore, the highest common factor of 20 and 30 is 10.
Example 2: The product of two numbers is 600. If their HCF is 10, what is their LCM?

Solution:

Given: HCF = 10 and product of numbers = 600
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 600/10
Therefore, the LCM is 60.
Example 3: For two numbers, HCF = 10 and LCM = 60. If one number is 30, find the other number.

Solution:

Given: HCF (x, 30) = 10 and LCM (x, 30) = 60
∵ HCF × LCM = 30 × (x)
⇒ x = (HCF × LCM)/30
⇒ x = (10 × 60)/30
⇒ x = 20
Therefore, the other number is 20.

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FAQs on HCF of 20 and 30

What is the HCF of 20 and 30?

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

If the HCF of 30 and 20 is 10, Find its LCM.

HCF(30, 20) × LCM(30, 20) = 30 × 20
Since the HCF of 30 and 20 = 10
⇒ 10 × LCM(30, 20) = 600
Therefore, LCM = 60
☛ Highest Common Factor Calculator

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

To find the HCF of 20 and 30, we will find the prime factorization of the given numbers, i.e. 20 = 2 × 2 × 5; 30 = 2 × 3 × 5.
⇒ Since 2, 5 are common terms in the prime factorization of 20 and 30. Hence, HCF(20, 30) = 2 × 5 = 10
☛ Prime Number

How to Find the HCF of 20 and 30 by Long Division Method?

To find the HCF of 20, 30 using long division method, 30 is divided by 20. The corresponding divisor (10) when remainder equals 0 is taken as HCF.

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

The following equation can be used to express the relation between Least Common Multiple and HCF of 20 and 30, i.e. HCF × LCM = 20 × 30.

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

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

By Long Division
By Euclidean Algorithm
By Prime Factorization

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