The Highest Common Factor (HCF) of 12 and 30 is 6. The HCF refers to the largest integer that can perfectly divide both given numbers. The factors of 12 and 30 are 1, 2, 3, 4, 6, 12 and 1, 2, 3, 5, 6, 10, 15, 30 respectively. The HCF of 12 and 30 can be found using prime factorisation, long division and listing common factors methods which are explained in this article in a comprehensive way for easy understanding.
HCF of 12 and 30 - Methods and Solved Examples | Testbook.com
Last Updated on Jun 13, 2024
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Understanding the HCF of 12 and 30
The HCF of 12 and 30 is 6. This article provides a clear explanation of how this HCF is derived using various methods. The HCF, 6, is the largest number that can exactly divide both 12 and 30.
Determining the HCF of 12 and 30
The following methods can be used to find the HCF of 12 and 30:
- Prime Factorisation
- Long Division method
- Listing common factors
Prime Factorisation Method for HCF of 12 and 30
The prime factorisation of 12 and 30 is expressed as:
12 = 2 × 2 × 3
30 = 2 × 3 × 5
The common prime factors of 12 and 30 are 2 and 3.
Hence, HCF (12, 30) = 2 × 3 = 6
Long Division Method for HCF of 12 and 30
In the long division method, the numbers (12, 30) are divided by prime factors. The HCF of 12 and 30 is the divisor we get after performing repeated long division until the remainder is zero.
Further division is not possible.
Therefore, HCF (12, 30) = 6
Listing Common Factors Method for HCF of 12 and 30
The method of listing common factors for determining the HCF of 12 and 30 is as follows:
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
The common factors of 12 and 30 are 1, 2, 3 and 6.
Hence, the highest common factor of 12 and 30 is 6.
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Frequently Asked Questions
What is the HCF of 12 and 30 if the LCM is 60?
The HCF is 6.
How to find the HCF of 12 and 30 using the long division method?
The HCF of 12 and 30 can be found using the long division method, by dividing 30 by 12. The divisor 6 we get when the remainder value is zero is the HCF.
What are the methods used to find HCF of 12 and 30?
The methods used to find the HCF of 12 and 30 are Long Division, Listing Common Factors and Prime Factorisation.
What is the HCF of 12 and 30?
The HCF of 12 and 30 is 6.
Show the relation between HCF and LCM of 12 and 30.
The relation between HCF and LCM of 12 and 30 is HCF × LCM = 12 × 30 = 360.
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