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HCF of 90 and 120

HCF of 90 and 120 is the largest possible number that divides 90 and 120 exactly without any remainder. The factors of 90 and 120 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 respectively. There are 3 commonly used methods to find the HCF of 90 and 120 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 90 and 120
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 90 and 120?

Answer: HCF of 90 and 120 is 30.

Explanation:

The HCF of two non-zero integers, x(90) and y(120), is the highest positive integer m(30) that divides both x(90) and y(120) without any remainder.

Methods to Find HCF of 90 and 120

The methods to find the HCF of 90 and 120 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

HCF of 90 and 120 by Long Division

HCF of 90 and 120 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 120 (larger number) by 90 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (90) by the remainder (30).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (30) is the HCF of 90 and 120.

HCF of 90 and 120 by Prime Factorization

Prime factorization of 90 and 120 is (2 × 3 × 3 × 5) and (2 × 2 × 2 × 3 × 5) respectively. As visible, 90 and 120 have common prime factors. Hence, the HCF of 90 and 120 is 2 × 3 × 5 = 30.

HCF of 90 and 120 by Listing Common Factors

Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

There are 8 common factors of 90 and 120, that are 1, 2, 3, 5, 6, 10, 15, and 30. Therefore, the highest common factor of 90 and 120 is 30.

☛ Also Check:

HCF of 90 and 120 Examples

Example 1: Find the HCF of 90 and 120, if their LCM is 360.

Solution:

∵ LCM × HCF = 90 × 120
⇒ HCF(90, 120) = (90 × 120)/360 = 30
Therefore, the highest common factor of 90 and 120 is 30.
Example 2: Find the highest number that divides 90 and 120 exactly.

Solution:

The highest number that divides 90 and 120 exactly is their highest common factor, i.e. HCF of 90 and 120.
⇒ Factors of 90 and 120:
- Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
- Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Therefore, the HCF of 90 and 120 is 30.
Example 3: The product of two numbers is 10800. If their HCF is 30, what is their LCM?

Solution:

Given: HCF = 30 and product of numbers = 10800
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 10800/30
Therefore, the LCM is 360.

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FAQs on HCF of 90 and 120

What is the HCF of 90 and 120?

The HCF of 90 and 120 is 30. To calculate the HCF of 90 and 120, we need to factor each number (factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90; factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120) and choose the highest factor that exactly divides both 90 and 120, i.e., 30.

What are the Methods to Find HCF of 90 and 120?

There are three commonly used methods to find the HCF of 90 and 120.

By Prime Factorization
By Long Division
By Listing Common Factors

How to Find the HCF of 90 and 120 by Long Division Method?

To find the HCF of 90, 120 using long division method, 120 is divided by 90. The corresponding divisor (30) when remainder equals 0 is taken as HCF.

How to Find the HCF of 90 and 120 by Prime Factorization?

To find the HCF of 90 and 120, we will find the prime factorization of the given numbers, i.e. 90 = 2 × 3 × 3 × 5; 120 = 2 × 2 × 2 × 3 × 5.
⇒ Since 2, 3, 5 are common terms in the prime factorization of 90 and 120. Hence, HCF(90, 120) = 2 × 3 × 5 = 30
☛ What is a Prime Number?

If the HCF of 120 and 90 is 30, Find its LCM.

HCF(120, 90) × LCM(120, 90) = 120 × 90
Since the HCF of 120 and 90 = 30
⇒ 30 × LCM(120, 90) = 10800
Therefore, LCM = 360
☛ Highest Common Factor Calculator

What is the Relation Between LCM and HCF of 90, 120?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 90 and 120, i.e. HCF × LCM = 90 × 120.

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