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HCF of 72 and 120

HCF of 72 and 120 is the largest possible number that divides 72 and 120 exactly without any remainder. The factors of 72 and 120 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 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 72 and 120 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 72 and 120
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 72 and 120?

Answer: HCF of 72 and 120 is 24.

Explanation:

The HCF of two non-zero integers, x(72) and y(120), is the highest positive integer m(24) that divides both x(72) and y(120) without any remainder.

Methods to Find HCF of 72 and 120

Let's look at the different methods for finding the HCF of 72 and 120.

Listing Common Factors
Prime Factorization Method
Using Euclid's Algorithm

HCF of 72 and 120 by Listing Common Factors

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
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 72 and 120, that are 1, 2, 3, 4, 6, 8, 12, and 24. Therefore, the highest common factor of 72 and 120 is 24.

HCF of 72 and 120 by Prime Factorization

Prime factorization of 72 and 120 is (2 × 2 × 2 × 3 × 3) and (2 × 2 × 2 × 3 × 5) respectively. As visible, 72 and 120 have common prime factors. Hence, the HCF of 72 and 120 is 2 × 2 × 2 × 3 = 24.

HCF of 72 and 120 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 = 120 and Y = 72

HCF(120, 72) = HCF(72, 120 mod 72) = HCF(72, 48)
HCF(72, 48) = HCF(48, 72 mod 48) = HCF(48, 24)
HCF(48, 24) = HCF(24, 48 mod 24) = HCF(24, 0)
HCF(24, 0) = 24 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 72 and 120 is 24.

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HCF of 72 and 120 Examples

Example 1: Find the HCF of 72 and 120, if their LCM is 360.

Solution:

∵ LCM × HCF = 72 × 120
⇒ HCF(72, 120) = (72 × 120)/360 = 24
Therefore, the highest common factor of 72 and 120 is 24.
Example 2: For two numbers, HCF = 24 and LCM = 360. If one number is 120, find the other number.

Solution:

Given: HCF (y, 120) = 24 and LCM (y, 120) = 360
∵ HCF × LCM = 120 × (y)
⇒ y = (HCF × LCM)/120
⇒ y = (24 × 360)/120
⇒ y = 72
Therefore, the other number is 72.
Example 3: The product of two numbers is 8640. If their HCF is 24, what is their LCM?

Solution:

Given: HCF = 24 and product of numbers = 8640
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 8640/24
Therefore, the LCM is 360.

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FAQs on HCF of 72 and 120

What is the HCF of 72 and 120?

The HCF of 72 and 120 is 24. To calculate the HCF (Highest Common Factor) of 72 and 120, we need to factor each number (factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72; 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 72 and 120, i.e., 24.

How to Find the HCF of 72 and 120 by Prime Factorization?

To find the HCF of 72 and 120, we will find the prime factorization of the given numbers, i.e. 72 = 2 × 2 × 2 × 3 × 3; 120 = 2 × 2 × 2 × 3 × 5.
⇒ Since 2, 2, 2, 3 are common terms in the prime factorization of 72 and 120. Hence, HCF(72, 120) = 2 × 2 × 2 × 3 = 24
☛ What are Prime Numbers?

What is the Relation Between LCM and HCF of 72, 120?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 72 and 120, i.e. HCF × LCM = 72 × 120.

What are the Methods to Find HCF of 72 and 120?

There are three commonly used methods to find the HCF of 72 and 120.

By Euclidean Algorithm
By Long Division
By Prime Factorization

How to Find the HCF of 72 and 120 by Long Division Method?

To find the HCF of 72, 120 using long division method, 120 is divided by 72. The corresponding divisor (24) when remainder equals 0 is taken as HCF.

If the HCF of 120 and 72 is 24, Find its LCM.

HCF(120, 72) × LCM(120, 72) = 120 × 72
Since the HCF of 120 and 72 = 24
⇒ 24 × LCM(120, 72) = 8640
Therefore, LCM = 360
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