China
Africa
Explore chapters and articles related to this topic
Data Structures and Manipulation
Published in Richard J. Roiger, Just Enough R!, 2020
The Euclidean algorithm provides an efficient way to find the greatest common divisor (GCD) of two positive integer numbers—the largest number that divides both numbers without a remainder. Write an iterative or recursive function to find the GCD. Here is the algorithm: Divide the smallest number into the largest number.If the remainder is 0, the divisor is the GCD and you are done.If there is a remainder, make the remainder the new smallest number and the divisor the new largest number. Repeat b.
Numbers and Elementary Mathematics
Published in Dan Zwillinger, CRC Standard Mathematical Tables and Formulas, 2018
The least common multiple of the integers a and b (denoted LCM(a,b) $ LCM(a, b) $ ) is the least integer r that is divisible by both a and b. The simplest way to find the LCM of a and b is via the formula LCM(a,b)=ab/GCD(a,b) $ LCM(a, b) = ab/GCD(a, b) $ . For example, LCM(10, 4) = 10·4GCD(10,4)=10·42=20. $ \frac{10 \cdot 4}{GCD(10,4)} = \frac{10 \cdot 4}{2} = 20. $
Network Reliability and Security
Published in Partha Pratim Sahu, Advances in Optical Networks and Components, 2020
Greatest common divisor: The greatest common divisor (gcd) of a pair of integers is the greater integer which divides both numbers of the given pair. Thus, 3 is the greatest common divisor of the pair (12,15). This is written as gcd (12,15) = 3.
The power of the snake: number theory with Python
Published in International Journal of Mathematical Education in Science and Technology, 2022
One of the first substantial results in number theory is that the greatest common divisor (gcd) is always a linear combination of its inputs. Students should learn how to find the coefficients of such a linear combination with the Euclidean Algorithm (Burton, 2010, p. 26). But besides doing this somewhat tedious computation by hand, there is also the power of code. After my students have mastered the Euclidean Algorithm with small numbers, I give them the following ‘extended gcd’ function, adapted from Extended Euclidean Algorithm (2021):