HCF of 27 and 45

The HCF of 27 and 45 is 9. The largest number that divides both 27 and 45 exactly without any remainder is defined as the Highest Common Factor (HCF) of 27 and 45. The common factors of 27 and 45 are 1, 3 and 9. Hence, 9 is the Highest Common Factor of 27 and 45. The article HCF is the best reference material for the students who wish to solve problems on HCF with speed and accuracy. In this article, let us look at the simple steps to calculate the Highest Common Factor of 27 and 45 using solved examples and FAQs in a detailed manner.

What is the HCF of 27 and 45?

The Highest Common Factor (HCF) of 27 and 45 is 9. This article explains how to find the Highest Common Factor of 27 and 45 using prime factorisation, long division method and listing common factors.

How to Find HCF of 27 and 45?

Let us look at the methods used to find the HCF of 27 and 45:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 27 and 45 by Prime Factorisation Method

In prime factorisation, the numbers can be expressed as the product of prime factors. Here, the numbers 27 and 45 are expressed as:

27 = 3 × 3 × 3

45 = 3 × 3 × 5

The common prime factors of 27 and 45 are 3 and 3.

Therefore,

HCF of (27, 45) = 3 × 3 = 9

HCF of 27 and 45 by Long Division Method

Go through the steps given below to find the Highest Common Factor of 27 and 45 using long division.

Step 1: Divide the largest number by the smallest among the given two numbers.

Step 2: Check the remainder; if it is not zero, then make it a new divisor and mention the previous divisor as the new dividend and continue the division process.

Step 3: Repeat this process until we get the remainder equal to zero. The last divisor is considered the HCF of the given two numbers.

The HCF of 27 and 45 by using the long division method is:

HCF of 27 and 45

HCF (27, 45) = 9

HCF of 27 and 45 by Listing Common Factors

In this method, we list out all the factors of 27 and 45 to find their HCF. The factors of 27 and 45 are given below:

Factors of 27: 1, 3, 9, 27

Factors of 45: 1, 3, 5, 9, 15, 45

Hence, HCF (27, 45) = 9

Related Articles

Video Lesson on Properties of HCF and LCM

Solved Examples

1. What is the highest number that divides both 27 and 45 exactly?

Solution: The highest number that divides both 27 and 45 exactly is their HCF. The factors of 27 and 45 are given below:

Factors of 27: 1, 3, 9, 27

Factors of 45: 1, 3, 5, 9, 15, 45

Hence, the HCF of 27 and 45 is 9.

2. What is the HCF of 27 and 45 if their LCM is 135?

Solution: Given 

LCM = 135

We know that

LCM × HCF = 27 × 45

HCF = (27 × 45) / LCM

HCF = (27 × 45) / 135

HCF = 9

Therefore, the HCF of 27 and 45 is 9.

Frequently Asked Questions on HCF of 27 and 45

Q1

What is the HCF of 27 and 45?

The HCF of 27 and 45 is 9.
Q2

Mention the methods used to find the HCF of 27 and 45.

There are three methods to find the HCF of 27 and 45. They are as follows:

Prime Factorisation

Long Division Method

Listing Common Factors

Q3

Is the HCF of 27 and 45 the same as the HCF of 9 and 27?

Yes. The HCF of 27 and 45 is 9, and the HCF of 9 and 27 is also 9.
Q4

Determine the LCM if the HCF of 27 and 45 is 9.

We know that

HCF × LCM = 27 × 45

Given

HCF = 9

9 × LCM = 27 × 45

LCM = 135

Q5

The HCF of 27 and 45 is 10. True or False.

False. The HCF of 27 and 45 is 9.

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