HCF of 18, 54 and 81

The HCF of 18, 54 and 81 is 9. The Highest Common Factor (HCF) is defined as the largest factor of two or more numbers. This number divides the given numbers exactly. The article HCF is formulated by professional teachers to help students enhance their skills in solving the problems of HCF and master the concept. Students who are in search of the best study tool can rely on this article and boost their knowledge of the HCF concept. Find the Highest Common Factor of 18, 54 and 81 along with solved examples and FAQs in this article.

What is the HCF of 18, 54 and 81?

The Highest Common Factor (HCF) of 18, 54 and 81 is 9. This article provides information on how to calculate the HCF of given numbers using prime factorisation, long division method and listing common factors.

How to Find HCF of 18, 54 and 81?

Let us glance at the methods used to find the HCF of 18, 54 and 81:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 18, 54 and 81 by Prime Factorisation Method

In the prime factorisation, we write the numbers as the product of prime factors to determine their HCF. Hence, the numbers 18, 54 and 81 are expressed as:

18 = 2 × 3 × 3

54 = 2 × 3 × 3 × 3

81 = 3 × 3 × 3 × 3

Common prime factors of 18, 54 and 81 are 3 and 3.

Therefore,

HCF (18, 54, 81) = 3 × 3 = 9

HCF of 18, 54 and 81 by Long Division Method

Follow the steps given below to find the Highest Common Factor of 18, 54 and 81 using the long division method.

Step 1: Divide the largest number 81 by the smallest number 18.

Step 2: We get the divisor as 9 when the remainder is equal to zero. Hence, the HCF of 18 and 81 is 9.

Step 3: Now, we perform the long division process on 9 and 54 to find the HCF. We get the divisor as 9 when the remainder is zero. Thus, the HCF of 9 and 54 is 9.

The HCF of 18, 54 and 81 by the long division method is;

First, calculate the HCF of 18 and 81

HCF of 18 54 and 81

HCF of 18 and 81 is 9 and HCF of 9 and 54 is 9

Hence, the HCF (18, 54, 81) = 9

HCF of 18, 54 and 81 by Listing the Factors

In this method, list out the factors of given numbers and choose the highest of all the common prime factors, as shown below:

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

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

Factors of 81: 1, 3, 9, 27, 81

Therefore, HCF (18, 54, 81) = 9

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Video Lesson on Properties of HCF and LCM

Solved Example

Question: What is the highest number that divides 18, 54 and 81 completely?

Solution: The largest number that divides 18, 54 and 81 completely is their Highest Common Factor (HCF). The factors of 18, 54 and 81 are:

 

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

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

Factors of 81: 1, 3, 9, 27, 81

The Highest Common Factor of 18, 54 and 81 is 9.

Hence, the highest number that divides 18, 54 and 81 completely is 9.

Frequently Asked Questions on HCF of 18, 54 and 81

Q1

What is the HCF of 18, 54 and 81?

The HCF of 18, 54 and 81 is 9.
Q2

Name the methods used to find the HCF of 18, 54 and 81.

There are three methods to find the HCF of 18, 54 and 81. They are as follows:

Prime Factorisation

Long Division method

Listing common factors

Q3

Is 362 the LCM of 18, 54 and 81?

No. The LCM of 18, 54 and 81 is 162.
Q4

The HCF of 18, 54 and 81 and the HCF of 9, 18 and 27 are the same. True or False.

True. The HCF of 18, 54 and 81 is 9 and the HCF of 9, 18 and 27 is also 9.
Q5

Find the HCF of 18, 54 and 81 using prime factorisation.

In the prime factorisation, to find the HCF, we express the given numbers as the product of prime factors

18 = 2 × 3 × 3

54 = 2 × 3 × 3 × 3

81 = 3 × 3 × 3 × 3

Common prime factors of 18, 54 and 81 are 3 and 3

Thus,the HCF (18, 54, 81) = 3 × 3 = 9

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