The HCF of 14 and 21 is 7. The Highest Common Factor (HCF) of 14 and 21 is the largest number that divides 14 and 21 evenly. Students who aspire to learn the HCF concept thoroughly can make use of the article HCF of Two Numbers prepared by BYJU’S teachers. This article explains the HCF concept in simple and understandable language so that students grasp the concept more effectively, irrespective of their intelligence quotient. Here, let us learn the simple steps to find the Highest Common Factor of 14 and 21 in a detailed manner.
What is the HCF 14 and 21?
The Highest Common Factor(HCF) or the Greatest Common Divisor (GCD) of 14 and 21 is 7. The only common prime factor of 14 and 21 is 7.
How to Find HCF of 14 and 21?
There are three methods to find the HCF of 14 and 21:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 14 and 21 by Prime Factorisation Method
In the prime factorisation method, we express the given numbers as the product of prime factors. Therefore, 14 and 21 can be expressed as:
14 = 2 × 7
21 = 3 × 7
The common prime factor of 14 and 21 is 7.
Therefore,
HCF (14, 21) = 7
HCF of 14 and 21 by Long Division Method
We use the following steps to find the Highest Common Factor of 14 and 21 in the long division method.
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 14 and 21 by the long division method is:
HCF (14, 21) = 7
HCF of 14 and 21 by Listing Common Factors
In this method, to find the HCF, we list out all the factors of 14 and 21. The factors of 14 and 21 are as follows:
Factors of 14:1, 2, 7, 14
Factors of 21: 1, 3, 7, 21
Hence, HCF (14, 21) = 7
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Video Lesson on Properties of HCF and LCM
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Solved Example
Question: The product of two numbers is 294. Find the LCM if their HCF is 7.
Solution: Given,
HCF = 7
Product of numbers = 294
We know that
HCF × LCM = Product of numbers
LCM = Product of numbers / HCF
LCM = 294 / 7
LCM = 42
Hence, the LCM is 42.
Frequently Asked Questions on HCF of 14 and 21
What is the HCF of 14 and 21?
Is the HCF of 14 and 21 the same as the HCF of 7 and 21?
What are the common prime factors of 14 and 21?
What are the methods used to determine the HCF of 14 and 21?
The methods used to determine the HCF of 14 and 21 are as follows:
Prime Factorisation
Long Division method
Listing common factors
If the HCF of 14 and 21 is 7, calculate their LCM.
We know that
HCF × LCM = 14 × 21
Given
HCF = 7
7 × LCM = 14 × 21
LCM = 42
Hence, the LCM is 42.
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