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HCF of 12 and 30

HCF of 12 and 30 is the largest possible number that divides 12 and 30 exactly without any remainder. The factors of 12 and 30 are 1, 2, 3, 4, 6, 12 and 1, 2, 3, 5, 6, 10, 15, 30 respectively. There are 3 commonly used methods to find the HCF of 12 and 30 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 12 and 30
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 12 and 30?

Answer: HCF of 12 and 30 is 6.

Explanation:

The HCF of two non-zero integers, x(12) and y(30), is the highest positive integer m(6) that divides both x(12) and y(30) without any remainder.

Methods to Find HCF of 12 and 30

The methods to find the HCF of 12 and 30 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

HCF of 12 and 30 by Prime Factorization

Prime factorization of 12 and 30 is (2 × 2 × 3) and (2 × 3 × 5) respectively. As visible, 12 and 30 have common prime factors. Hence, the HCF of 12 and 30 is 2 × 3 = 6.

HCF of 12 and 30 by Listing Common Factors

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

There are 4 common factors of 12 and 30, that are 1, 2, 3, and 6. Therefore, the highest common factor of 12 and 30 is 6.

HCF of 12 and 30 by Long Division

HCF of 12 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 12 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (6).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (6) is the HCF of 12 and 30.

☛ Also Check:

HCF of 12 and 30 Examples

Example 1: Find the HCF of 12 and 30, if their LCM is 60.

Solution:

∵ LCM × HCF = 12 × 30
⇒ HCF(12, 30) = (12 × 30)/60 = 6
Therefore, the highest common factor of 12 and 30 is 6.
Example 2: The product of two numbers is 360. If their HCF is 6, what is their LCM?

Solution:

Given: HCF = 6 and product of numbers = 360
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 360/6
Therefore, the LCM is 60.
Example 3: Find the highest number that divides 12 and 30 exactly.

Solution:

The highest number that divides 12 and 30 exactly is their highest common factor, i.e. HCF of 12 and 30.
⇒ Factors of 12 and 30:
- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Therefore, the HCF of 12 and 30 is 6.

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FAQs on HCF of 12 and 30

What is the HCF of 12 and 30?

The HCF of 12 and 30 is 6. To calculate the Highest common factor of 12 and 30, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30) and choose the highest factor that exactly divides both 12 and 30, i.e., 6.

How to Find the HCF of 12 and 30 by Long Division Method?

To find the HCF of 12, 30 using long division method, 30 is divided by 12. The corresponding divisor (6) when remainder equals 0 is taken as HCF.

If the HCF of 30 and 12 is 6, Find its LCM.

HCF(30, 12) × LCM(30, 12) = 30 × 12
Since the HCF of 30 and 12 = 6
⇒ 6 × LCM(30, 12) = 360
Therefore, LCM = 60
☛ Highest Common Factor Calculator

How to Find the HCF of 12 and 30 by Prime Factorization?

To find the HCF of 12 and 30, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 30 = 2 × 3 × 5.
⇒ Since 2, 3 are common terms in the prime factorization of 12 and 30. Hence, HCF(12, 30) = 2 × 3 = 6
☛ Prime Number

What are the Methods to Find HCF of 12 and 30?

There are three commonly used methods to find the HCF of 12 and 30.

By Euclidean Algorithm
By Long Division
By Prime Factorization

What is the Relation Between LCM and HCF of 12, 30?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 12 and 30, i.e. HCF × LCM = 12 × 30.

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