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HCF of 12 and 24

HCF of 12 and 24 is the largest possible number that divides 12 and 24 exactly without any remainder. The factors of 12 and 24 are 1, 2, 3, 4, 6, 12 and 1, 2, 3, 4, 6, 8, 12, 24 respectively. There are 3 commonly used methods to find the HCF of 12 and 24 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 12 and 24
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 12 and 24?

Answer: HCF of 12 and 24 is 12.

Explanation:

The HCF of two non-zero integers, x(12) and y(24), is the highest positive integer m(12) that divides both x(12) and y(24) without any remainder.

Methods to Find HCF of 12 and 24

Let's look at the different methods for finding the HCF of 12 and 24.

Listing Common Factors
Long Division Method
Prime Factorization Method

HCF of 12 and 24 by Listing Common Factors

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

There are 6 common factors of 12 and 24, that are 1, 2, 3, 4, 6, and 12. Therefore, the highest common factor of 12 and 24 is 12.

HCF of 12 and 24 by Long Division

HCF of 12 and 24 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 24 (larger number) by 12 (smaller number).
Step 2: Since the remainder = 0, the divisor (12) is the HCF of 12 and 24.

The corresponding divisor (12) is the HCF of 12 and 24.

HCF of 12 and 24 by Prime Factorization

Prime factorization of 12 and 24 is (2 × 2 × 3) and (2 × 2 × 2 × 3) respectively. As visible, 12 and 24 have common prime factors. Hence, the HCF of 12 and 24 is 2 × 2 × 3 = 12.

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HCF of 12 and 24 Examples

Example 1: Find the highest number that divides 12 and 24 exactly.

Solution:

The highest number that divides 12 and 24 exactly is their highest common factor, i.e. HCF of 12 and 24.
⇒ Factors of 12 and 24:
- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
Therefore, the HCF of 12 and 24 is 12.
Example 2: The product of two numbers is 288. If their HCF is 12, what is their LCM?

Solution:

Given: HCF = 12 and product of numbers = 288
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 288/12
Therefore, the LCM is 24.
Example 3: For two numbers, HCF = 12 and LCM = 24. If one number is 12, find the other number.

Solution:

Given: HCF (x, 12) = 12 and LCM (x, 12) = 24
∵ HCF × LCM = 12 × (x)
⇒ x = (HCF × LCM)/12
⇒ x = (12 × 24)/12
⇒ x = 24
Therefore, the other number is 24.

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FAQs on HCF of 12 and 24

What is the HCF of 12 and 24?

The HCF of 12 and 24 is 12. To calculate the Highest common factor of 12 and 24, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24) and choose the highest factor that exactly divides both 12 and 24, i.e., 12.

What is the Relation Between LCM and HCF of 12, 24?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 12 and 24, i.e. HCF × LCM = 12 × 24.

What are the Methods to Find HCF of 12 and 24?

There are three commonly used methods to find the HCF of 12 and 24.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the HCF of 12 and 24 by Long Division Method?

To find the HCF of 12, 24 using long division method, 24 is divided by 12. The corresponding divisor (12) when remainder equals 0 is taken as HCF.

If the HCF of 24 and 12 is 12, Find its LCM.

HCF(24, 12) × LCM(24, 12) = 24 × 12
Since the HCF of 24 and 12 = 12
⇒ 12 × LCM(24, 12) = 288
Therefore, LCM = 24
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How to Find the HCF of 12 and 24 by Prime Factorization?

To find the HCF of 12 and 24, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 24 = 2 × 2 × 2 × 3.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 12 and 24. Hence, HCF(12, 24) = 2 × 2 × 3 = 12
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