Use Euclid's Division Algorithm to find the HCF of 867 and 255 || Class X Maths

Use Euclid's Division Algorithm to find the HCF of 867 and 255 || Class X Maths Exersice 1.1 Q.(iii)
------------------------------------------------------
How to find HCF using Euclid's Division Algorithm. Real Number
-------------------------------------------
Your Query:
How to find hcf by Euclid's division algorithm
Euclid's division algorithm
Euclidean algorithm in number theory
How to do extended Euclidean algorithm
Algorithm for multiplication
how to do hcf in maths
Algorithm mathematics
how to find hcf of big number
division algorithm example
algorithm to find the factorial of a number
how to find factor of a number
algorithm to find sum of digits of a number
------------------------------------------
Find HCF using Euclidean Division Algorithm | Step-by-Step Tutorial

Welcome to this video where we dive into the Euclidean Division Algorithm to find the Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), of two numbers. This classic method is one of the most efficient ways to compute the HCF and has been a foundational algorithm in mathematics for centuries.

What Will You Learn?
In this video, we will:

Explain what HCF (or GCD) is and why it’s important.
Break down the Euclidean Division Algorithm step by step.
Work through examples to show how this algorithm helps to find the HCF of two numbers.
Explain the mathematical basis of the algorithm and why it works.
Provide a quick overview of the Extended Euclidean Algorithm, which is useful in solving Diophantine equations and cryptographic problems.
Why Use the Euclidean Algorithm?
The Euclidean Algorithm is not only simple but also highly efficient, especially when dealing with large numbers. Its beauty lies in the fact that it reduces the problem size at each step by using the remainder of divisions. This process continues until the remainder becomes zero, and the last non-zero remainder is the HCF.

How Does It Work?
The algorithm can be summarized in three simple steps:

Divide the larger number by the smaller number and get the quotient and remainder.
Replace the larger number with the smaller number and the smaller number with the remainder.
Repeat the process until the remainder is zero. The last non-zero remainder is the HCF.
We’ll walk you through several examples to show exactly how this works in practice!

Examples Included:
Finding the HCF of two small numbers (e.g., 56 and 98).
Solving more complex cases with larger numbers.
Brief introduction to how the Extended Euclidean Algorithm can find the coefficients to express the HCF as a linear combination of the two numbers, which is crucial in cryptography and number theory.
Why Is This Important?
The Euclidean Algorithm has a wide range of practical applications, from cryptography (RSA algorithm) to solving mathematical problems involving divisibility and integer solutions. It also serves as a fundamental tool in computer science and algorithm design.

Whether you’re a student preparing for exams or someone interested in learning more about number theory, this tutorial will give you a solid understanding of how to compute the HCF using the Euclidean method.

What’s Next?
Don’t forget to:

Like the video if it helped you understand the Euclidean Division Algorithm!
Subscribe for more math tutorials, algorithms, and problem-solving tips.
Comment below if you have any questions or want to see more examples!
Let’s simplify HCF calculation using the power of Euclid’s timeless algorithm!