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HCF of 36 and 144

HCF of 36 and 144 is the largest possible number that divides 36 and 144 exactly without any remainder. The factors of 36 and 144 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 respectively. There are 3 commonly used methods to find the HCF of 36 and 144 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 36 and 144
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 36 and 144?

Answer: HCF of 36 and 144 is 36.

Explanation:

The HCF of two non-zero integers, x(36) and y(144), is the highest positive integer m(36) that divides both x(36) and y(144) without any remainder.

Methods to Find HCF of 36 and 144

The methods to find the HCF of 36 and 144 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

HCF of 36 and 144 by Listing Common Factors

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

There are 9 common factors of 36 and 144, that are 1, 2, 3, 4, 36, 6, 9, 12, and 18. Therefore, the highest common factor of 36 and 144 is 36.

HCF of 36 and 144 by Prime Factorization

Prime factorization of 36 and 144 is (2 × 2 × 3 × 3) and (2 × 2 × 2 × 2 × 3 × 3) respectively. As visible, 36 and 144 have common prime factors. Hence, the HCF of 36 and 144 is 2 × 2 × 3 × 3 = 36.

HCF of 36 and 144 by Long Division

HCF of 36 and 144 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 144 (larger number) by 36 (smaller number).
Step 2: Since the remainder = 0, the divisor (36) is the HCF of 36 and 144.

The corresponding divisor (36) is the HCF of 36 and 144.

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HCF of 36 and 144 Examples

Example 1: For two numbers, HCF = 36 and LCM = 144. If one number is 36, find the other number.

Solution:

Given: HCF (x, 36) = 36 and LCM (x, 36) = 144
∵ HCF × LCM = 36 × (x)
⇒ x = (HCF × LCM)/36
⇒ x = (36 × 144)/36
⇒ x = 144
Therefore, the other number is 144.
Example 2: The product of two numbers is 5184. If their HCF is 36, what is their LCM?

Solution:

Given: HCF = 36 and product of numbers = 5184
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 5184/36
Therefore, the LCM is 144.
Example 3: Find the HCF of 36 and 144, if their LCM is 144.

Solution:

∵ LCM × HCF = 36 × 144
⇒ HCF(36, 144) = (36 × 144)/144 = 36
Therefore, the highest common factor of 36 and 144 is 36.

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FAQs on HCF of 36 and 144

What is the HCF of 36 and 144?

The HCF of 36 and 144 is 36. To calculate the Highest common factor of 36 and 144, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144) and choose the highest factor that exactly divides both 36 and 144, i.e., 36.

How to Find the HCF of 36 and 144 by Long Division Method?

To find the HCF of 36, 144 using long division method, 144 is divided by 36. The corresponding divisor (36) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 36, 144?

The following equation can be used to express the relation between LCM and HCF of 36 and 144, i.e. HCF × LCM = 36 × 144.

If the HCF of 144 and 36 is 36, Find its LCM.

HCF(144, 36) × LCM(144, 36) = 144 × 36
Since the HCF of 144 and 36 = 36
⇒ 36 × LCM(144, 36) = 5184
Therefore, LCM = 144
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What are the Methods to Find HCF of 36 and 144?

There are three commonly used methods to find the HCF of 36 and 144.

By Listing Common Factors
By Prime Factorization
By Long Division

How to Find the HCF of 36 and 144 by Prime Factorization?

To find the HCF of 36 and 144, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 144 = 2 × 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 2, 3, 3 are common terms in the prime factorization of 36 and 144. Hence, HCF(36, 144) = 2 × 2 × 3 × 3 = 36
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