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HCF of 18 and 54

HCF of 18 and 54 is the largest possible number that divides 18 and 54 exactly without any remainder. The factors of 18 and 54 are 1, 2, 3, 6, 9, 18 and 1, 2, 3, 6, 9, 18, 27, 54 respectively. There are 3 commonly used methods to find the HCF of 18 and 54 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 18 and 54
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 18 and 54?

Answer: HCF of 18 and 54 is 18.

Explanation:

The HCF of two non-zero integers, x(18) and y(54), is the highest positive integer m(18) that divides both x(18) and y(54) without any remainder.

Methods to Find HCF of 18 and 54

The methods to find the HCF of 18 and 54 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

HCF of 18 and 54 by Listing Common Factors

Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54

There are 6 common factors of 18 and 54, that are 1, 2, 3, 6, 9, and 18. Therefore, the highest common factor of 18 and 54 is 18.

HCF of 18 and 54 by Prime Factorization

Prime factorization of 18 and 54 is (2 × 3 × 3) and (2 × 3 × 3 × 3) respectively. As visible, 18 and 54 have common prime factors. Hence, the HCF of 18 and 54 is 2 × 3 × 3 = 18.

HCF of 18 and 54 by Long Division

HCF of 18 and 54 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 54 (larger number) by 18 (smaller number).
Step 2: Since the remainder = 0, the divisor (18) is the HCF of 18 and 54.

The corresponding divisor (18) is the HCF of 18 and 54.

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HCF of 18 and 54 Examples

Example 1: For two numbers, HCF = 18 and LCM = 54. If one number is 54, find the other number.

Solution:

Given: HCF (y, 54) = 18 and LCM (y, 54) = 54
∵ HCF × LCM = 54 × (y)
⇒ y = (HCF × LCM)/54
⇒ y = (18 × 54)/54
⇒ y = 18
Therefore, the other number is 18.
Example 2: The product of two numbers is 972. If their HCF is 18, what is their LCM?

Solution:

Given: HCF = 18 and product of numbers = 972
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 972/18
Therefore, the LCM is 54.
Example 3: Find the highest number that divides 18 and 54 exactly.

Solution:

The highest number that divides 18 and 54 exactly is their highest common factor, i.e. HCF of 18 and 54.
⇒ Factors of 18 and 54:
- Factors of 18 = 1, 2, 3, 6, 9, 18
- Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54
Therefore, the HCF of 18 and 54 is 18.

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FAQs on HCF of 18 and 54

What is the HCF of 18 and 54?

The HCF of 18 and 54 is 18. To calculate the Highest common factor of 18 and 54, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54) and choose the highest factor that exactly divides both 18 and 54, i.e., 18.

What is the Relation Between LCM and HCF of 18, 54?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 18 and 54, i.e. HCF × LCM = 18 × 54.

How to Find the HCF of 18 and 54 by Long Division Method?

To find the HCF of 18, 54 using long division method, 54 is divided by 18. The corresponding divisor (18) when remainder equals 0 is taken as HCF.

How to Find the HCF of 18 and 54 by Prime Factorization?

To find the HCF of 18 and 54, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 54 = 2 × 3 × 3 × 3.
⇒ Since 2, 3, 3 are common terms in the prime factorization of 18 and 54. Hence, HCF(18, 54) = 2 × 3 × 3 = 18
☛ What is a Prime Number?

What are the Methods to Find HCF of 18 and 54?

There are three commonly used methods to find the HCF of 18 and 54.

By Long Division
By Prime Factorization
By Listing Common Factors

If the HCF of 54 and 18 is 18, Find its LCM.

HCF(54, 18) × LCM(54, 18) = 54 × 18
Since the HCF of 54 and 18 = 18
⇒ 18 × LCM(54, 18) = 972
Therefore, LCM = 54
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