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HCF of 120 and 150

HCF of 120 and 150 is the largest possible number that divides 120 and 150 exactly without any remainder. The factors of 120 and 150 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 and 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150 respectively. There are 3 commonly used methods to find the HCF of 120 and 150 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 120 and 150
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 120 and 150?

Answer: HCF of 120 and 150 is 30.

Explanation:

The HCF of two non-zero integers, x(120) and y(150), is the highest positive integer m(30) that divides both x(120) and y(150) without any remainder.

Methods to Find HCF of 120 and 150

The methods to find the HCF of 120 and 150 are explained below.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

HCF of 120 and 150 by Prime Factorization

Prime factorization of 120 and 150 is (2 × 2 × 2 × 3 × 5) and (2 × 3 × 5 × 5) respectively. As visible, 120 and 150 have common prime factors. Hence, the HCF of 120 and 150 is 2 × 3 × 5 = 30.

HCF of 120 and 150 by Long Division

HCF of 120 and 150 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 150 (larger number) by 120 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (120) by the remainder (30).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (30) is the HCF of 120 and 150.

HCF of 120 and 150 by Euclidean Algorithm

As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 150 and Y = 120

HCF(150, 120) = HCF(120, 150 mod 120) = HCF(120, 30)
HCF(120, 30) = HCF(30, 120 mod 30) = HCF(30, 0)
HCF(30, 0) = 30 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 120 and 150 is 30.

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HCF of 120 and 150 Examples

Example 1: Find the HCF of 120 and 150, if their LCM is 600.

Solution:

∵ LCM × HCF = 120 × 150
⇒ HCF(120, 150) = (120 × 150)/600 = 30
Therefore, the highest common factor of 120 and 150 is 30.
Example 2: Find the highest number that divides 120 and 150 exactly.

Solution:

The highest number that divides 120 and 150 exactly is their highest common factor, i.e. HCF of 120 and 150.
⇒ Factors of 120 and 150:
- Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
- Factors of 150 = 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Therefore, the HCF of 120 and 150 is 30.
Example 3: For two numbers, HCF = 30 and LCM = 600. If one number is 120, find the other number.

Solution:

Given: HCF (z, 120) = 30 and LCM (z, 120) = 600
∵ HCF × LCM = 120 × (z)
⇒ z = (HCF × LCM)/120
⇒ z = (30 × 600)/120
⇒ z = 150
Therefore, the other number is 150.

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FAQs on HCF of 120 and 150

What is the HCF of 120 and 150?

The HCF of 120 and 150 is 30. To calculate the Highest common factor of 120 and 150, 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 150 = 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150) and choose the highest factor that exactly divides both 120 and 150, i.e., 30.

What are the Methods to Find HCF of 120 and 150?

There are three commonly used methods to find the HCF of 120 and 150.

By Prime Factorization
By Listing Common Factors
By Long Division

If the HCF of 150 and 120 is 30, Find its LCM.

HCF(150, 120) × LCM(150, 120) = 150 × 120
Since the HCF of 150 and 120 = 30
⇒ 30 × LCM(150, 120) = 18000
Therefore, LCM = 600
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How to Find the HCF of 120 and 150 by Prime Factorization?

To find the HCF of 120 and 150, we will find the prime factorization of the given numbers, i.e. 120 = 2 × 2 × 2 × 3 × 5; 150 = 2 × 3 × 5 × 5.
⇒ Since 2, 3, 5 are common terms in the prime factorization of 120 and 150. Hence, HCF(120, 150) = 2 × 3 × 5 = 30
☛ What is a Prime Number?

How to Find the HCF of 120 and 150 by Long Division Method?

To find the HCF of 120, 150 using long division method, 150 is divided by 120. The corresponding divisor (30) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 120, 150?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 120 and 150, i.e. HCF × LCM = 120 × 150.

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