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HCF of 24 and 36

HCF of 24 and 36 is the largest possible number that divides 24 and 36 exactly without any remainder. The factors of 24 and 36 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively. There are 3 commonly used methods to find the HCF of 24 and 36 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 24 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 24 and 36?

Answer: HCF of 24 and 36 is 12.

Explanation:

The HCF of two non-zero integers, x(24) and y(36), is the highest positive integer m(12) that divides both x(24) and y(36) without any remainder.

Methods to Find HCF of 24 and 36

Let's look at the different methods for finding the HCF of 24 and 36.

Prime Factorization Method
Listing Common Factors
Long Division Method

HCF of 24 and 36 by Prime Factorization

Prime factorization of 24 and 36 is (2 × 2 × 2 × 3) and (2 × 2 × 3 × 3) respectively. As visible, 24 and 36 have common prime factors. Hence, the HCF of 24 and 36 is 2 × 2 × 3 = 12.

HCF of 24 and 36 by Listing Common Factors

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

There are 6 common factors of 24 and 36, that are 1, 2, 3, 4, 6, and 12. Therefore, the highest common factor of 24 and 36 is 12.

HCF of 24 and 36 by Long Division

HCF of 24 and 36 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 36 (larger number) by 24 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (24) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (12) is the HCF of 24 and 36.

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HCF of 24 and 36 Examples

Example 1: The product of two numbers is 864. If their HCF is 12, what is their LCM?

Solution:

Given: HCF = 12 and product of numbers = 864
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 864/12
Therefore, the LCM is 72.
Example 2: Find the HCF of 24 and 36, if their LCM is 72.

Solution:

∵ LCM × HCF = 24 × 36
⇒ HCF(24, 36) = (24 × 36)/72 = 12
Therefore, the highest common factor of 24 and 36 is 12.
Example 3: Find the highest number that divides 24 and 36 exactly.

Solution:

The highest number that divides 24 and 36 exactly is their highest common factor, i.e. HCF of 24 and 36.
⇒ Factors of 24 and 36:
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Therefore, the HCF of 24 and 36 is 12.

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FAQs on HCF of 24 and 36

What is the HCF of 24 and 36?

The HCF of 24 and 36 is 12. To calculate the Highest common factor of 24 and 36, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the highest factor that exactly divides both 24 and 36, i.e., 12.

What are the Methods to Find HCF of 24 and 36?

There are three commonly used methods to find the HCF of 24 and 36.

By Long Division
By Listing Common Factors
By Prime Factorization

If the HCF of 36 and 24 is 12, Find its LCM.

HCF(36, 24) × LCM(36, 24) = 36 × 24
Since the HCF of 36 and 24 = 12
⇒ 12 × LCM(36, 24) = 864
Therefore, LCM = 72
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How to Find the HCF of 24 and 36 by Long Division Method?

To find the HCF of 24, 36 using long division method, 36 is divided by 24. The corresponding divisor (12) when remainder equals 0 is taken as HCF.

How to Find the HCF of 24 and 36 by Prime Factorization?

To find the HCF of 24 and 36, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 36 = 2 × 2 × 3 × 3.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 24 and 36. Hence, HCF(24, 36) = 2 × 2 × 3 = 12
☛ What are Prime Numbers?

What is the Relation Between LCM and HCF of 24, 36?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 24 and 36, i.e. HCF × LCM = 24 × 36.

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