The HCF of 18 and 54 is 18. The largest number that divides 18 and 54 exactly without any remainder is termed the Highest Common Factor of 18 and 54. The article HCF of Two Numbers is the best source to grasp in-depth knowledge of HCF. Students who face difficulty in finding the HCF of two numbers can follow this article and get their doubts cleared quickly. There are 6 common factors of 18 and 54. They are 1, 2, 3, 6, 9 and 18. Clearly, 18 is the Highest Common Factor of 18 and 54. Let us learn in detail how to find the Highest Common Factor of 18 and 54, along with solved examples and FAQs here.
What is the HCF of 18 and 54?
The Highest Common Factor (HCF) or the Greatest Common Divisor (GCD) of 18 and 54 is 18. 1, 2, 3, 6, 9 and 18 are the six common factors of 18 and 54.
How to Find HCF of 18 and 54?
To find the HCF of 18 and 54, we use the following three methods:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 18 and 54 by Prime Factorisation Method
In this method, we express the given numbers as the product of prime factors. Thus, 18 and 54 can be written as shown below:
18 = 2 × 3 × 3
54 = 2 × 3 × 3 × 3
The common prime factors of 18 and 54 are 2, 3 and 3.
Hence,
HCF (18, 54) = 2 × 3 × 3 = 18
HCF of 18 and 54 by Long Division Method
Follow the steps mentioned below to find the Highest Common Factor of 18 and 54 in the long division method.
Step 1: Divide the largest number by the smallest number from the given two numbers.
Step 2: Now, check the remainder. If it is not zero, then make it a new divisor and write the previous divisor as the new dividend. Then perform the division.
Step 3: Repeat this process until the remainder becomes zero. The last divisor will be the HCF of the given two numbers.
The HCF of 18 and 54 using the long division method is as follows:
Thus, HCF (18, 54) = 18
HCF of 18 and 54 by Listing Common Factors
In this method, we can determine the Highest Common Factor by listing all the factors of given numbers. The factors of 18 and 54 are mentioned below:
Factors of 18:1, 2, 3, 6, 9, 18
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
Therefore, HCF (18, 54) = 18
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Solved Examples
1. Determine the highest number that divides both 18 and 54 exactly.
Solution: The highest number that divides 18 and 54 exactly is their HCF. To determine the HCF, we need to list factors 18 and 54 as below:
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
Clearly, the HCF of 18 and 54 is 18. Therefore, 18 is the highest number that divides both 18 and 54 exactly.
2. The product of the two numbers is 972, and their HCF is 18. Calculate their LCM.
Solution:
Given
HCF = 18
Product of numbers = 972
We know that
LCM × HCF = Product of numbers
LCM × 18 = 972
LCM = 972 / 18
LCM = 972 / 18 = 54
Therefore, the LCM of 18 and 54 is 54.
Frequently Asked Questions on HCF of 18 and 54
What is the HCF of 18 and 54?
Is the LCM of 18 and 54 and the HCF of 18 and 54 the same?
Write the methods to find the HCF of 18 and 54.
The following methods are used to find the HCF of 18 and 54:
Prime Factorisation
Long Division method
Listing common factors
How to find the HCF of 18 and 54 by prime factorisation?
In this method, we write the given numbers as the product of prime factors as below:
18 = 2 × 3 × 3
54 = 2 × 3 × 3 × 3
The common prime factors of 18 and 54 are 2, 3 and 3
Hence,
HCF (18, 54) = 2 × 3 × 3 = 18
Therefore, by prime factorisation, the HCF of 18 and 54 is 18
What is the LCM if the HCF of 18 and 54 is 18?
We know that
HCF × LCM = 18 × 54
Given
HCF = 18
18 × LCM = 18 × 54
LCM = 18
Therefore, the LCM is 18
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