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HCF of 60 and 72

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

1.	HCF of 60 and 72
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 60 and 72?

Answer: HCF of 60 and 72 is 12.

Explanation:

The HCF of two non-zero integers, x(60) and y(72), is the highest positive integer m(12) that divides both x(60) and y(72) without any remainder.

Methods to Find HCF of 60 and 72

Let's look at the different methods for finding the HCF of 60 and 72.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

HCF of 60 and 72 by Long Division

HCF of 60 and 72 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 72 (larger number) by 60 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (60) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (12) is the HCF of 60 and 72.

HCF of 60 and 72 by Listing Common Factors

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

There are 6 common factors of 60 and 72, that are 1, 2, 3, 4, 6, and 12. Therefore, the highest common factor of 60 and 72 is 12.

HCF of 60 and 72 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 = 72 and Y = 60

HCF(72, 60) = HCF(60, 72 mod 60) = HCF(60, 12)
HCF(60, 12) = HCF(12, 60 mod 12) = HCF(12, 0)
HCF(12, 0) = 12 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 60 and 72 is 12.

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HCF of 60 and 72 Examples

Example 1: For two numbers, HCF = 12 and LCM = 360. If one number is 60, find the other number.

Solution:

Given: HCF (z, 60) = 12 and LCM (z, 60) = 360
∵ HCF × LCM = 60 × (z)
⇒ z = (HCF × LCM)/60
⇒ z = (12 × 360)/60
⇒ z = 72
Therefore, the other number is 72.
Example 2: The product of two numbers is 4320. If their HCF is 12, what is their LCM?

Solution:

Given: HCF = 12 and product of numbers = 4320
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 4320/12
Therefore, the LCM is 360.
Example 3: Find the HCF of 60 and 72, if their LCM is 360.

Solution:

∵ LCM × HCF = 60 × 72
⇒ HCF(60, 72) = (60 × 72)/360 = 12
Therefore, the highest common factor of 60 and 72 is 12.

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FAQs on HCF of 60 and 72

What is the HCF of 60 and 72?

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

If the HCF of 72 and 60 is 12, Find its LCM.

HCF(72, 60) × LCM(72, 60) = 72 × 60
Since the HCF of 72 and 60 = 12
⇒ 12 × LCM(72, 60) = 4320
Therefore, LCM = 360
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What are the Methods to Find HCF of 60 and 72?

There are three commonly used methods to find the HCF of 60 and 72.

By Euclidean Algorithm
By Long Division
By Prime Factorization

How to Find the HCF of 60 and 72 by Long Division Method?

To find the HCF of 60, 72 using long division method, 72 is divided by 60. The corresponding divisor (12) when remainder equals 0 is taken as HCF.

How to Find the HCF of 60 and 72 by Prime Factorization?

To find the HCF of 60 and 72, we will find the prime factorization of the given numbers, i.e. 60 = 2 × 2 × 3 × 5; 72 = 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 60 and 72. Hence, HCF(60, 72) = 2 × 2 × 3 = 12
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What is the Relation Between LCM and HCF of 60, 72?

The following equation can be used to express the relation between LCM and HCF of 60 and 72, i.e. HCF × LCM = 60 × 72.

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