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HCF of 12 and 36

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

1.	HCF of 12 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 12 and 36?

Answer: HCF of 12 and 36 is 12.

Explanation:

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

Methods to Find HCF of 12 and 36

Let's look at the different methods for finding the HCF of 12 and 36.

Listing Common Factors
Long Division Method
Prime Factorization Method

HCF of 12 and 36 by Listing Common Factors

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

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

HCF of 12 and 36 by Long Division

HCF of 12 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 12 (smaller number).
Step 2: Since the remainder = 0, the divisor (12) is the HCF of 12 and 36.

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

HCF of 12 and 36 by Prime Factorization

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

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HCF of 12 and 36 Examples

Example 1: The product of two numbers is 432. If their HCF is 12, what is their LCM?

Solution:

Given: HCF = 12 and product of numbers = 432
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 432/12
Therefore, the LCM is 36.
Example 2: Find the HCF of 12 and 36, if their LCM is 36.

Solution:

∵ LCM × HCF = 12 × 36
⇒ HCF(12, 36) = (12 × 36)/36 = 12
Therefore, the highest common factor of 12 and 36 is 12.
Example 3: For two numbers, HCF = 12 and LCM = 36. If one number is 36, find the other number.

Solution:

Given: HCF (y, 36) = 12 and LCM (y, 36) = 36
∵ HCF × LCM = 36 × (y)
⇒ y = (HCF × LCM)/36
⇒ y = (12 × 36)/36
⇒ y = 12
Therefore, the other number is 12.

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FAQs on HCF of 12 and 36

What is the HCF of 12 and 36?

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

What is the Relation Between LCM and HCF of 12, 36?

The following equation can be used to express the relation between Least Common Multiple and HCF of 12 and 36, i.e. HCF × LCM = 12 × 36.

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

HCF(36, 12) × LCM(36, 12) = 36 × 12
Since the HCF of 36 and 12 = 12
⇒ 12 × LCM(36, 12) = 432
Therefore, LCM = 36
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What are the Methods to Find HCF of 12 and 36?

There are three commonly used methods to find the HCF of 12 and 36.

By Euclidean Algorithm
By Long Division
By Prime Factorization

How to Find the HCF of 12 and 36 by Prime Factorization?

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

How to Find the HCF of 12 and 36 by Long Division Method?

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

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