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HCF of 18 and 27

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

1.	HCF of 18 and 27
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 18 and 27?

Answer: HCF of 18 and 27 is 9.

Explanation:

The HCF of two non-zero integers, x(18) and y(27), is the highest positive integer m(9) that divides both x(18) and y(27) without any remainder.

Methods to Find HCF of 18 and 27

The methods to find the HCF of 18 and 27 are explained below.

Long Division Method
Listing Common Factors
Prime Factorization Method

HCF of 18 and 27 by Long Division

HCF of 18 and 27 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 27 (larger number) by 18 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (9).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (9) is the HCF of 18 and 27.

HCF of 18 and 27 by Listing Common Factors

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

There are 3 common factors of 18 and 27, that are 1, 3, and 9. Therefore, the highest common factor of 18 and 27 is 9.

HCF of 18 and 27 by Prime Factorization

Prime factorization of 18 and 27 is (2 × 3 × 3) and (3 × 3 × 3) respectively. As visible, 18 and 27 have common prime factors. Hence, the HCF of 18 and 27 is 3 × 3 = 9.

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HCF of 18 and 27 Examples

Example 1: Find the highest number that divides 18 and 27 exactly.

Solution:

The highest number that divides 18 and 27 exactly is their highest common factor, i.e. HCF of 18 and 27.
⇒ Factors of 18 and 27:
- Factors of 18 = 1, 2, 3, 6, 9, 18
- Factors of 27 = 1, 3, 9, 27
Therefore, the HCF of 18 and 27 is 9.
Example 2: For two numbers, HCF = 9 and LCM = 54. If one number is 27, find the other number.

Solution:

Given: HCF (y, 27) = 9 and LCM (y, 27) = 54
∵ HCF × LCM = 27 × (y)
⇒ y = (HCF × LCM)/27
⇒ y = (9 × 54)/27
⇒ y = 18
Therefore, the other number is 18.
Example 3: Find the HCF of 18 and 27, if their LCM is 54.

Solution:

∵ LCM × HCF = 18 × 27
⇒ HCF(18, 27) = (18 × 27)/54 = 9
Therefore, the highest common factor of 18 and 27 is 9.

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FAQs on HCF of 18 and 27

What is the HCF of 18 and 27?

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

What is the Relation Between LCM and HCF of 18, 27?

The following equation can be used to express the relation between Least Common Multiple and HCF of 18 and 27, i.e. HCF × LCM = 18 × 27.

If the HCF of 27 and 18 is 9, Find its LCM.

HCF(27, 18) × LCM(27, 18) = 27 × 18
Since the HCF of 27 and 18 = 9
⇒ 9 × LCM(27, 18) = 486
Therefore, LCM = 54
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What are the Methods to Find HCF of 18 and 27?

There are three commonly used methods to find the HCF of 18 and 27.

By Prime Factorization
By Euclidean Algorithm
By Long Division

How to Find the HCF of 18 and 27 by Long Division Method?

To find the HCF of 18, 27 using long division method, 27 is divided by 18. The corresponding divisor (9) when remainder equals 0 is taken as HCF.

How to Find the HCF of 18 and 27 by Prime Factorization?

To find the HCF of 18 and 27, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 27 = 3 × 3 × 3.
⇒ Since 3, 3 are common terms in the prime factorization of 18 and 27. Hence, HCF(18, 27) = 3 × 3 = 9
☛ What is a Prime Number?

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