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HCF of 108 and 144

HCF of 108 and 144 is the largest possible number that divides 108 and 144 exactly without any remainder. The factors of 108 and 144 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 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 108 and 144 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 108 and 144
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 108 and 144?

Answer: HCF of 108 and 144 is 36.

Explanation:

The HCF of two non-zero integers, x(108) and y(144), is the highest positive integer m(36) that divides both x(108) and y(144) without any remainder.

Methods to Find HCF of 108 and 144

The methods to find the HCF of 108 and 144 are explained below.

Listing Common Factors
Long Division Method
Prime Factorization Method

HCF of 108 and 144 by Listing Common Factors

Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

There are 9 common factors of 108 and 144, that are 1, 2, 3, 4, 36, 6, 9, 12, and 18. Therefore, the highest common factor of 108 and 144 is 36.

HCF of 108 and 144 by Long Division

HCF of 108 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 108 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (108) by the remainder (36).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (36) is the HCF of 108 and 144.

HCF of 108 and 144 by Prime Factorization

Prime factorization of 108 and 144 is (2 × 2 × 3 × 3 × 3) and (2 × 2 × 2 × 2 × 3 × 3) respectively. As visible, 108 and 144 have common prime factors. Hence, the HCF of 108 and 144 is 2 × 2 × 3 × 3 = 36.

☛ Also Check:

HCF of 108 and 144 Examples

Example 1: Find the highest number that divides 108 and 144 exactly.

Solution:

The highest number that divides 108 and 144 exactly is their highest common factor, i.e. HCF of 108 and 144.
⇒ Factors of 108 and 144:
- Factors of 108 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
- Factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Therefore, the HCF of 108 and 144 is 36.
Example 2: Find the HCF of 108 and 144, if their LCM is 432.

Solution:

∵ LCM × HCF = 108 × 144
⇒ HCF(108, 144) = (108 × 144)/432 = 36
Therefore, the highest common factor of 108 and 144 is 36.
Example 3: The product of two numbers is 15552. If their HCF is 36, what is their LCM?

Solution:

Given: HCF = 36 and product of numbers = 15552
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 15552/36
Therefore, the LCM is 432.

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FAQs on HCF of 108 and 144

What is the HCF of 108 and 144?

The HCF of 108 and 144 is 36. To calculate the HCF of 108 and 144, we need to factor each number (factors of 108 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108; 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 108 and 144, i.e., 36.

How to Find the HCF of 108 and 144 by Prime Factorization?

To find the HCF of 108 and 144, we will find the prime factorization of the given numbers, i.e. 108 = 2 × 2 × 3 × 3 × 3; 144 = 2 × 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 2, 3, 3 are common terms in the prime factorization of 108 and 144. Hence, HCF(108, 144) = 2 × 2 × 3 × 3 = 36
☛ What is a Prime Number?

If the HCF of 144 and 108 is 36, Find its LCM.

HCF(144, 108) × LCM(144, 108) = 144 × 108
Since the HCF of 144 and 108 = 36
⇒ 36 × LCM(144, 108) = 15552
Therefore, LCM = 432
☛ Highest Common Factor Calculator

How to Find the HCF of 108 and 144 by Long Division Method?

To find the HCF of 108, 144 using long division method, 144 is divided by 108. The corresponding divisor (36) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 108, 144?

The following equation can be used to express the relation between LCM and HCF of 108 and 144, i.e. HCF × LCM = 108 × 144.

What are the Methods to Find HCF of 108 and 144?

There are three commonly used methods to find the HCF of 108 and 144.

By Listing Common Factors
By Prime Factorization
By Long Division

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