The HCF of 12 and 24 is 12. The greatest number that divides the given numbers exactly without leaving a remainder is called the Highest Common Factor. The article on HCF, prepared by BYJU’S experts in simple language, is the perfect guide to enhance the skills of solving complex problems related to HCF without any obstacles. We can find the Highest Common Factor of 12 and 24 using methods such as prime factorisation, long division method, and listing common factors. Let us understand the simple method of how to verify the Highest Common Factor of 12 and 24 using solved examples and FAQs in this article.
What is the HCF of 12 and 24?
The Highest Common Factor of 12 and 24 is 12. There are six common factors of 12 and 24. They are 1, 2, 3, 4, 6, and 12. Here, 12 is the largest number. Hence the Highest Common Factor of 12 and 24 is 12.
How to Find HCF of 12 and 24?
There are three methods to find the HCF of 12 and 24:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 12 and 24 by Prime Factorisation Method
To determine the HCF using prime factorisation, we write the numbers as the product of prime factors. Therefore the numbers 12 and 24 are expressed as;
12 = 2 × 2 × 3
24 = 2 × 2 × 2 × 3
Common Factors of 12 and 24 are 2, 2 and 3.
Therefore,
HCF (12, 24) = 2 × 2 × 3 = 12
HCF of 12 and 24 by Long Division Method
In this method, we use the steps given below to find the Highest Common Factor of 12 and 24
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 0, then make it a new divisor and write the previous divisor as the new dividend. Then continue the division process.
Step 3: Repeat this process until we get the remainder equal to zero. The last divisor will be the HCF of the given two numbers.
The Highest Common Factor of 12 and 24 by long division method is;
HCF (12, 24) = 12
HCF of 12 and 24 by Listing the Factors
We list all the factors of 12 and 24 to verify their Highest Common Factor. The factors of 12 and 24 are provided below:
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Therefore, HCF (12, 24) = 12
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Video Lesson on Properties of HCF and LCM
Solved Example
Question: What is the highest number that divides both 12 and 24 exactly?
Solution: The highest number that divides both 12 and 24 is their HCF. We know that 12 is the Highest Common Factor of 12 and 24. Hence, 12 is the highest number that divides 12 and 24 exactly.
Frequently Asked Questions on HCF of 12 and 24
What is the HCF of 12 and 24?
What are the common factors of 12 and 24?
List out the methods used to find the HCF of 12 and 24.
The methods used to find the HCF of 12 and 24 are as follows:
Prime Factorisation
Long Division method
Listing common factors
What is the LCM if the HCF of 12 and 24 is 12?
We know that
HCF × LCM = 12 × 24
Given
HCF = 12
12 × LCM = 12 × 24
LCM = 24
Therefore, the LCM is 24
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