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 (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
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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
What is the HCF of 27 and 45?
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
Is the HCF of 27 and 45 the same as the HCF of 9 and 27?
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
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