The HCF of 8 and 12 is 4. The Highest Common Factor of two or more numbers is defined as the largest positive integer that divides the numbers without leaving a remainder. In the given set of numbers 8 and 12, 4 is the Greatest Common Factor (GCF) that divides both 8 and 12. Thus, we can say the Highest Common Factor of 8 and 12 is 4. To learn more about Highest Common Factor (HCF), refer to the article HCF designed by BYJU’S experts. Let us understand the simple steps of how to find the Highest Common Factor of 8 and 12 in detail in this article.
What is the HCF of 8 and 12?
The Highest Common Factor of 8 and 12 is 4. The numbers 1, 2, and 4 are the three common factors of 8 and 12. Therefore the Highest Common Factor of 8 and 12 is 4.
How to Find HCF of 8 and 12?
There are three methods to find the HCF of 8 and 12:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 8 and 12 by Prime Factorisation Method
In the prime factorisation, to find the HCF, we express the given numbers as the product of prime factors. Hence, 8 and 12 can be expressed as;
8 = 2 × 2 × 2
12 = 2 × 2 × 3
Common prime factors of 8 and 12 are 2 and 2.
Therefore, HCF (8, 12) = 2 × 2 = 4
HCF of 8 and 12 by Long Division Method
The following steps are used to find the Highest Common Factor of 8 and 12:
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 perform the division.
Step 3: Continue this process until we get the remainder as zero. The last divisor will be the HCF of the given two numbers.
The Highest Common Factor of 8 and 12 by the long division method is;
HCF (8, 12) = 4
HCF of 8 and 12 by Listing the Factors
Here, we list out the common factors of 8 and 12 to find their HCF. The factors of 8 and 12 are as follows:
Factors of 8: 1, 2, 4, 8
Factors of 12: 1, 2, 3, 4, 6, 12
Therefore, HCF (8, 12) = 4
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Video Lesson on Properties of HCF and LCM
Solved Example
Question: What is the HCF of 8 and 12 if their LCM is 24?
Solution: Given
LCM = 24
We know that
LCM × HCF = 8 × 12
HCF (8, 12) = (8 × 12)/LCM
HCF (8, 12) = (8 × 12)/24
HCF (8, 12) = 4
Hence the Highest Common Factor of 8 and 12 is 4.
Frequently Asked Questions on HCF of 8 and 12
What is the HCF of 8 and 12?
What are the common factors of 8 and 12?
Name the methods used to find the HCF of 8 and 12.
The methods used to find the HCF of 8 and 12 are as follows:
Prime Factorisation
Long Division method
Listing common factors
Write the relation between LCM and HCF of 8 and 12.
The below equation is used to denote the relation between LCM and HCF of 8 and 12
HCF × LCM = 8 × 12
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