The HCF of 12 and 14 is 2. HCF stands for Highest Common Factor. It is also called the Greatest Common Divisor (GCD). Highest Common Factor is one of the best articles prepared by BYJU’S experts to clear the doubts of students while solving problems on HCF. Students can make use of this article for effective learning of the HCF concept. Learn the simple methods to find the Highest Common Factor of 12 and 14 with the help of solved examples and FAQs in an accurate manner here.
What is the HCF of 12 and 14?
The Highest Common Factor of 12 and 14 is 2. In this article, we will learn how to find the Highest Common Factor of 12 and 14 using three methods. They are prime factorisation, long division method and listing common factors.
How to Find HCF of 12 and 14?
There are three methods to find the HCF of 12 and 14:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 12 and 14 by Prime Factorisation Method
In the prime factorisation, to find the HCF, we express the given numbers as the product of prime factors. Therefore, 12 and 14 can be expressed as:
12 = 2 × 2 × 3
14 = 2 × 7
The common prime factor of 12 and 14 is 2.
Therefore,
HCF (12, 14) = 2
HCF of 12 and 14 by Long Division Method
In the long division method, we use the following steps to find the HCF of 12 and 14.
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 we get the remainder equal to zero. The last divisor will be the HCF of the given two numbers.
The HCF of 12 and 14 by the long division method is shown below:
HCF (12, 14) = 2
HCF of 12 and 14 by Listing Common Factors
In this method, we list out the common factors of 12 and 14 to find their HCF. The common factors of 12 and 14 are as follows:
Factors of 12:1, 2, 3, 4, 6, 12
Factors of 14: 1, 2, 7, 14
Hence, HCF (12, 14) = 2
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Video Lesson on Properties of HCF and LCM
Solved Examples
1. What is the greatest number that divides both 12 and 14 exactly?
Solution: 2 is the greatest number that divides both 12 and 14 exactly.
2. What is the LCM if the product of two numbers is 168 and their GCF is 2?
Solution: Given,
GCF = 2
Product of two numbers = 168
LCM × GCF = Product of two numbers
LCM = Product of two numbers / GCF
LCM = 168/2
LCM = 84
Hence, the LCM is 84.
Frequently Asked Questions on HCF of 12 and 14
What is the HCF of 12 and 14?
How to find the HCF of 12 and 14 by prime factorisation?
Here, we express the given numbers as the product of prime factors. Thus, the numbers 12 and 14 can be expressed as:
12 = 2 × 2 × 3
14 = 2 × 7
HCF (12, 14) = 2
Name the methods to find the HCF of 12 and 14.
The methods used to find the HCF of 12 and 14 are as follows:
Prime Factorisation
Long Division method
Listing common factors
What is the LCM if the HCF of 12 and 14 is 2?
We know that
HCF × LCM = 12 × 14
Given
HCF = 2
2 × LCM = 12 × 14
LCM = 84
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