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HCF of 144 and 180

HCF of 144 and 180 is the largest possible number that divides 144 and 180 exactly without any remainder. The factors of 144 and 180 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 and 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 respectively. There are 3 commonly used methods to find the HCF of 144 and 180 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 144 and 180
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 144 and 180?

Answer: HCF of 144 and 180 is 36.

Explanation:

The HCF of two non-zero integers, x(144) and y(180), is the highest positive integer m(36) that divides both x(144) and y(180) without any remainder.

Methods to Find HCF of 144 and 180

The methods to find the HCF of 144 and 180 are explained below.

Long Division Method
Listing Common Factors
Prime Factorization Method

HCF of 144 and 180 by Long Division

HCF of 144 and 180 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 180 (larger number) by 144 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (144) by the remainder (36).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (36) is the HCF of 144 and 180.

HCF of 144 and 180 by Listing Common Factors

Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

There are 9 common factors of 144 and 180, that are 1, 2, 3, 4, 36, 6, 9, 12, and 18. Therefore, the highest common factor of 144 and 180 is 36.

HCF of 144 and 180 by Prime Factorization

Prime factorization of 144 and 180 is (2 × 2 × 2 × 2 × 3 × 3) and (2 × 2 × 3 × 3 × 5) respectively. As visible, 144 and 180 have common prime factors. Hence, the HCF of 144 and 180 is 2 × 2 × 3 × 3 = 36.

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HCF of 144 and 180 Examples

Example 1: Find the HCF of 144 and 180, if their LCM is 720.

Solution:

∵ LCM × HCF = 144 × 180
⇒ HCF(144, 180) = (144 × 180)/720 = 36
Therefore, the highest common factor of 144 and 180 is 36.
Example 2: For two numbers, HCF = 36 and LCM = 720. If one number is 144, find the other number.

Solution:

Given: HCF (z, 144) = 36 and LCM (z, 144) = 720
∵ HCF × LCM = 144 × (z)
⇒ z = (HCF × LCM)/144
⇒ z = (36 × 720)/144
⇒ z = 180
Therefore, the other number is 180.
Example 3: The product of two numbers is 25920. If their HCF is 36, what is their LCM?

Solution:

Given: HCF = 36 and product of numbers = 25920
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 25920/36
Therefore, the LCM is 720.

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FAQs on HCF of 144 and 180

What is the HCF of 144 and 180?

The HCF of 144 and 180 is 36. To calculate the Highest common factor of 144 and 180, we need to factor each number (factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144; factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180) and choose the highest factor that exactly divides both 144 and 180, i.e., 36.

What is the Relation Between LCM and HCF of 144, 180?

The following equation can be used to express the relation between LCM and HCF of 144 and 180, i.e. HCF × LCM = 144 × 180.

How to Find the HCF of 144 and 180 by Long Division Method?

To find the HCF of 144, 180 using long division method, 180 is divided by 144. The corresponding divisor (36) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 144 and 180?

There are three commonly used methods to find the HCF of 144 and 180.

By Prime Factorization
By Listing Common Factors
By Long Division

If the HCF of 180 and 144 is 36, Find its LCM.

HCF(180, 144) × LCM(180, 144) = 180 × 144
Since the HCF of 180 and 144 = 36
⇒ 36 × LCM(180, 144) = 25920
Therefore, LCM = 720
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How to Find the HCF of 144 and 180 by Prime Factorization?

To find the HCF of 144 and 180, we will find the prime factorization of the given numbers, i.e. 144 = 2 × 2 × 2 × 2 × 3 × 3; 180 = 2 × 2 × 3 × 3 × 5.
⇒ Since 2, 2, 3, 3 are common terms in the prime factorization of 144 and 180. Hence, HCF(144, 180) = 2 × 2 × 3 × 3 = 36
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