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Lecture 8

Lecture 8. Greatest Common Divisors & Least Common Multiples Definition 4 Let a and b be integers, not both zero. The largest integer d such that d|a and d|b is called the greatest common divisor of a and b. It is denoted gcd (a, b). Example: gcd (24, 36)

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Chapter 2 The Fundamentals: Algorithms, the Integers, and Matrices

Chapter 2 The Fundamentals: Algorithms, the Integers, and Matrices. Algorithm : specifying a sequence of steps used to solve a problem. Computational complexity of an algorithm : what are the computer resources needed to use this algorithm to solve a problem of a specified size?

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Chapter 2 (Part 1): The Fundamentals: Algorithms, the Integers & Matrices

Chapter 2 (Part 1): The Fundamentals: Algorithms, the Integers & Matrices. The Integers and Division (Section 2.4). Introduction Review basics concepts of number theory Divisibility, greatest common divisors, modular arithmetic Computer arithmetic using binary expansions

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Chapter 3 (Part 2): The Fundamentals: Algorithms, the Integers & Matrices

Chapter 3 (Part 2): The Fundamentals: Algorithms, the Integers & Matrices. The Integers and Division (Section 3.4). Introduction Review basics concepts of number theory Divisibility, greatest common divisors, modular arithmetic Computer arithmetic using binary expansions

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Section 2.4

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Integers

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Quantification

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