The HCF of 3 and 12 is 3. The largest positive integer that divides the numbers without leaving a remainder is represented as the Highest Common Factor. In the given set of numbers 3 and 12, 3 is the highest number that divides both 3 and 12 exactly. Therefore, we can say that the Highest Common Factor of 3 and 12 is 3. To gain proficiency in the HCF concept, students can refer to the article Highest Common Factor designed by the expert faculty in simple and understandable language. Let us learn the simple procedure of how to determine the Highest Common Factor of 3 and 12 in this article.
What is the HCF of 3 and 12?
The Highest Common Factor of 3 and 12 is 3. The numbers 1 and 3 are the common factors of 3 and 12. Therefore, the Highest Common Factor of 3 and 12 is 3.
How to Find HCF of 3 and 12?
There are three methods to find the HCF of 3 and 12:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 3 and 12 by Prime Factorisation Method
In prime factorisation, to find the HCF, we express the given numbers as the product of prime factors. Thus, 3 and 12 can be expressed as:
3 = 3
12 = 2 × 2 × 3
The common prime factor of 3 and 12 is 3.
Therefore, HCF (3, 12) = 3
HCF of 3 and 12 by Long Division Method
The below steps are used to find the Highest Common Factor of 3 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 3 and 12 by the long division method is as follows:
HCF (3, 12) = 3
HCF of 3 and 12 by Listing Common Factors
In this method, we list out the common factors of 3 and 12 to find their HCF. The factors of 3 and 12 are as follows:
Factors of 3:1, 3
Factors of 12: 1, 2, 3, 4, 6, 12
Therefore, HCF (3, 12) = 3
Related Articles
Video Lesson on Properties of HCF and LCM
Solved Example
Question: What is the HCF of 3 and 12 if their LCM is 12?
Solution: Given,
LCM = 12
We know that:
LCM × HCF = 3 × 12
12 × HCF = 3 × 12
HCF= 3
Hence, the Highest Common Factor of 3 and 12 is 3.
Frequently Asked Questions on HCF of 3 and 12
What is the HCF of 3 and 12?
How to find the HCF of 3 and 12 using prime factorisation?
To find the HCF by using prime factorisation, we write the numbers as the product of prime factors.
Name the methods used to find the HCF of 3 and 12.
The methods used to find the HCF of 3 and 12 are as follows:
Prime Factorisation
Long Division method
Listing common factors
Mention the relation between LCM and HCF of 3 and 12.
The below equation is used to depict the relation between LCM and HCF of 3 and 12:
HCF × LCM = 3 × 12
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