HCF of 21 and 29 is 1. The largest number that divides both 21 and 29 exactly is defined as the Highest Common Factor (HCF) of 21 and 29. The article HCF of Two Numbers offers detailed information relying on the HCF concept in simple and understandable language. Students can access this article both online and offline anytime to improve their skills in HCF calculation. Following this article on a regular basis enable students to solve any HCF problem effortlessly. Let us grasp the simple procedure of how to determine the Highest Common Factor of 21 and 29 along with solved examples and FAQs in this article.
What is HCF 21 and 29?
The Highest Common Factor(HCF) or the Greatest Common Divisor (GCD) of 21 and 29 is 1. The factors of 21 are 1, 3, 7, 21 and the factors of 29 are 1, 29 respectively.
How to Find HCF of 21 and 29?
The following three methods are used to find the HCF of 21 and 29:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 21 and 29 by Prime Factorisation Method
In the prime factorisation method, we represent the given numbers as the product of prime factors to determine their HCF. Therefore, 21 and 29 can be written as;
21 = 3 × 7
29 = 29
There is no common prime factor between 21 and 29.
Therefore,
HCF (21, 29) = 1
HCF of 21 and 29 by Long Division Method
We use the below steps to find the Highest Common Factor of 21 and 29 in the 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 21 and 29 by the long division method is as follows;
HCF (21, 29) = 1
HCF of 21 and 29 by Listing the Factors
In this method, to obtain the HCF, we list out all the factors of given numbers. The following are the factors of 21 and 29:
Factors of 21:1, 3, 7, 21
Factors of 29: 1, 29
Hence, HCF (21, 29) = 1
Related Articles
Video Lesson on Properties of HCF and LCM
Solved Example
Question: What is the LCM if the product of two numbers is 609 and their HCF is 1?
Solution: Given
HCF = 1
Product of numbers = 609
We know that
HCF × LCM = Product of numbers
LCM = Product of numbers / HCF
LCM = 609/1
LCM = 609
Hence the LCM is 609.
Frequently Asked Questions on HCF of 21 and 29
What is the HCF of 21 and 29?
Is the HCF of 21 and 29 the same as the HCF of 7 and 3?
Mention the relation between LCM and HCF of 21 and 29.
To express the relation between LCM and HCF of 21 and 29, we use the following equation
HCF × LCM = 21 × 29
List out the methods used to determine the HCF of 21 and 29.
The methods used to determine the HCF of 21 and 29 are as follows:
Prime Factorisation
Long Division method
Listing common factors
If the HCF of 21 and 29 is 1. What is their LCM?
We know that
HCF × LCM = 21 × 29
Given
HCF = 1
1 × LCM = 21 × 29
LCM = 609
Therefore, the LCM is 609.
Comments