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HCF of 120 and 144

HCF of 120 and 144 is the largest possible number that divides 120 and 144 exactly without any remainder. The factors of 120 and 144 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 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 120 and 144 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 120 and 144
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 120 and 144?

Answer: HCF of 120 and 144 is 24.

Explanation:

The HCF of two non-zero integers, x(120) and y(144), is the highest positive integer m(24) that divides both x(120) and y(144) without any remainder.

Methods to Find HCF of 120 and 144

The methods to find the HCF of 120 and 144 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

HCF of 120 and 144 by Prime Factorization

Prime factorization of 120 and 144 is (2 × 2 × 2 × 3 × 5) and (2 × 2 × 2 × 2 × 3 × 3) respectively. As visible, 120 and 144 have common prime factors. Hence, the HCF of 120 and 144 is 2 × 2 × 2 × 3 = 24.

HCF of 120 and 144 by Listing Common Factors

Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

There are 8 common factors of 120 and 144, that are 1, 2, 3, 4, 6, 8, 12, and 24. Therefore, the highest common factor of 120 and 144 is 24.

HCF of 120 and 144 by Long Division

HCF of 120 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 120 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (120) by the remainder (24).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (24) is the HCF of 120 and 144.

☛ Also Check:

HCF of 120 and 144 Examples

Example 1: For two numbers, HCF = 24 and LCM = 720. If one number is 120, find the other number.

Solution:

Given: HCF (z, 120) = 24 and LCM (z, 120) = 720
∵ HCF × LCM = 120 × (z)
⇒ z = (HCF × LCM)/120
⇒ z = (24 × 720)/120
⇒ z = 144
Therefore, the other number is 144.
Example 2: Find the highest number that divides 120 and 144 exactly.

Solution:

The highest number that divides 120 and 144 exactly is their highest common factor, i.e. HCF of 120 and 144.
⇒ Factors of 120 and 144:
- Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
- Factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Therefore, the HCF of 120 and 144 is 24.
Example 3: Find the HCF of 120 and 144, if their LCM is 720.

Solution:

∵ LCM × HCF = 120 × 144
⇒ HCF(120, 144) = (120 × 144)/720 = 24
Therefore, the highest common factor of 120 and 144 is 24.

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FAQs on HCF of 120 and 144

What is the HCF of 120 and 144?

The HCF of 120 and 144 is 24. To calculate the HCF (Highest Common Factor) of 120 and 144, we need to factor each number (factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120; 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 120 and 144, i.e., 24.

What are the Methods to Find HCF of 120 and 144?

There are three commonly used methods to find the HCF of 120 and 144.

By Listing Common Factors
By Prime Factorization
By Long Division

How to Find the HCF of 120 and 144 by Long Division Method?

To find the HCF of 120, 144 using long division method, 144 is divided by 120. The corresponding divisor (24) when remainder equals 0 is taken as HCF.

How to Find the HCF of 120 and 144 by Prime Factorization?

To find the HCF of 120 and 144, we will find the prime factorization of the given numbers, i.e. 120 = 2 × 2 × 2 × 3 × 5; 144 = 2 × 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 2, 2, 3 are common terms in the prime factorization of 120 and 144. Hence, HCF(120, 144) = 2 × 2 × 2 × 3 = 24
☛ Prime Number

If the HCF of 144 and 120 is 24, Find its LCM.

HCF(144, 120) × LCM(144, 120) = 144 × 120
Since the HCF of 144 and 120 = 24
⇒ 24 × LCM(144, 120) = 17280
Therefore, LCM = 720
☛ Highest Common Factor Calculator

What is the Relation Between LCM and HCF of 120, 144?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 120 and 144, i.e. HCF × LCM = 120 × 144.

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