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HCF of 18 and 60

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

1.	HCF of 18 and 60
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 18 and 60?

Answer: HCF of 18 and 60 is 6.

Explanation:

The HCF of two non-zero integers, x(18) and y(60), is the highest positive integer m(6) that divides both x(18) and y(60) without any remainder.

Methods to Find HCF of 18 and 60

Let's look at the different methods for finding the HCF of 18 and 60.

Listing Common Factors
Prime Factorization Method
Long Division Method

HCF of 18 and 60 by Listing Common Factors

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

There are 4 common factors of 18 and 60, that are 1, 2, 3, and 6. Therefore, the highest common factor of 18 and 60 is 6.

HCF of 18 and 60 by Prime Factorization

Prime factorization of 18 and 60 is (2 × 3 × 3) and (2 × 2 × 3 × 5) respectively. As visible, 18 and 60 have common prime factors. Hence, the HCF of 18 and 60 is 2 × 3 = 6.

HCF of 18 and 60 by Long Division

HCF of 18 and 60 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 60 (larger number) by 18 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (6).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (6) is the HCF of 18 and 60.

☛ Also Check:

HCF of 18 and 60 Examples

Example 1: Find the highest number that divides 18 and 60 exactly.

Solution:

The highest number that divides 18 and 60 exactly is their highest common factor, i.e. HCF of 18 and 60.
⇒ Factors of 18 and 60:
- Factors of 18 = 1, 2, 3, 6, 9, 18
- Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Therefore, the HCF of 18 and 60 is 6.
Example 2: For two numbers, HCF = 6 and LCM = 180. If one number is 60, find the other number.

Solution:

Given: HCF (y, 60) = 6 and LCM (y, 60) = 180
∵ HCF × LCM = 60 × (y)
⇒ y = (HCF × LCM)/60
⇒ y = (6 × 180)/60
⇒ y = 18
Therefore, the other number is 18.
Example 3: The product of two numbers is 1080. If their HCF is 6, what is their LCM?

Solution:

Given: HCF = 6 and product of numbers = 1080
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 1080/6
Therefore, the LCM is 180.

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FAQs on HCF of 18 and 60

What is the HCF of 18 and 60?

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

What is the Relation Between LCM and HCF of 18, 60?

The following equation can be used to express the relation between LCM and HCF of 18 and 60, i.e. HCF × LCM = 18 × 60.

How to Find the HCF of 18 and 60 by Long Division Method?

To find the HCF of 18, 60 using long division method, 60 is divided by 18. The corresponding divisor (6) when remainder equals 0 is taken as HCF.

If the HCF of 60 and 18 is 6, Find its LCM.

HCF(60, 18) × LCM(60, 18) = 60 × 18
Since the HCF of 60 and 18 = 6
⇒ 6 × LCM(60, 18) = 1080
Therefore, LCM = 180
☛ Highest Common Factor Calculator

How to Find the HCF of 18 and 60 by Prime Factorization?

To find the HCF of 18 and 60, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 60 = 2 × 2 × 3 × 5.
⇒ Since 2, 3 are common terms in the prime factorization of 18 and 60. Hence, HCF(18, 60) = 2 × 3 = 6
☛ Prime Numbers

What are the Methods to Find HCF of 18 and 60?

There are three commonly used methods to find the HCF of 18 and 60.

By Prime Factorization
By Euclidean Algorithm
By Long Division

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