Multiplicative functions

Greatest common divisor

In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted . For example, the GCD of 8 and 12 is 4, that is, . In the name "greatest common divisor", the adjective "greatest" may be replaced by "highest", and the word "divisor" may be replaced by "factor", so that other names include highest common factor (hcf), etc. Historically, other names for the same concept have included greatest common measure. This notion can be extended to polynomials (see Polynomial greatest common divisor) and other commutative rings (see below). (Wikipedia).

Greatest common divisor
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Introduction to Number Theory, Part 2: Greatest Common Divisors

The second video in a series about elementary number theory. We define the greatest common divisor of two numbers, and prove a useful theorem.

From playlist Introduction to Number Theory

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Introduction to number theory lecture 4. More on Euclid's algorithm

This lecture is part of my Berkeley math 115 course "Introduction to number theory" We discuss how to solve linear equations in integers using Euclid's algorithm. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 The textb

From playlist Introduction to number theory (Berkeley Math 115)

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Theory of numbers: Euclid's algorithm

This lecture is part of an online undergraduate course on the theory of numbers. We describe several algorithms for finding the greatest common divisor of two numbers. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52Qf7lc3HHvHRdIysxEcj1H

From playlist Theory of numbers

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Lecture 6 - Divisibility and Primes

This is Lecture 6 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2006.pdf More information may

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Relatively Prime Fibonacci Numbers

Today we solve a number theory problem involving Fibonacci numbers and the Fibonacci sequence! We will prove that consecutive Fibonacci numbers are relatively prime (also called coprime or mutual primes), this means their greatest common divisor is 1. We prove this using induction and the

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Introduction to number theory lecture 3: Divisibility and Euclid's algorithms.

This lecture is part of my Berkeley math 115 course "Introduction to number theory" The lecture covers basic properties of divisibility, and Euclid's algorithm for finding greatest common divisors. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EF

From playlist Introduction to number theory (Berkeley Math 115)

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Discrete Math - 4.3.2 Greatest Common Divisors and Least Common Multiples

Finding the greatest common divisor and least common multiple using the method of primes. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz

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Coding Challenge 161: Estimating π from Random Numbers with Euclid's Algorithm

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Basic Methods: We develop basic properties of the integers, with a focus on divisibility. Main results include Bezout's identity, unique factorization of integers into primes, and the definition of modular integers.

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Greatest common factor exercise | Factors and multiples | Pre-Algebra | Khan Academy

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