Lab 15.1 Greatest Common Divisor A formula for finding the greatest common divisor (GCD) of two numbers was formulated by the mathematician Euclid around 300 BCE. The GCD of two numbers is the largest number that will divide into both numbers without any remainder. For example, the GCD of 12 and 16 is 4, the GCD of 18 and 12 is 6. The basic algorithm is as follows: Assume we are computing the GCD of two integers x and y. Follow the steps below: 1. Replace the larger of x and y with the remainder after (integer) dividing the larger number by the smaller one. 2. If x or y is zero, stop. The answer is the nonzero value. 3 If neither x nor y is zero, go back to step 1. Here is an example listing the successive values of x and y: XIII O 135 15 15 0 y 20 20 5 5 } (135/ 20) = 15 (20 / 15) = 5 (15 / 5) = 0 GCD = 5 Write a recursive method that finds the GCD of two numbers using Euclid's algorithm. public class Arithmetic { public static int gcd (int a, int b) { // Your work here Lab 15.2 Tester for GCD Write a tester program for your GCD algorithm.
Lab 15.1 Greatest Common Divisor A formula for finding the greatest common divisor (GCD) of two numbers was formulated by the mathematician Euclid around 300 BCE. The GCD of two numbers is the largest number that will divide into both numbers without any remainder. For example, the GCD of 12 and 16 is 4, the GCD of 18 and 12 is 6. The basic algorithm is as follows: Assume we are computing the GCD of two integers x and y. Follow the steps below: 1. Replace the larger of x and y with the remainder after (integer) dividing the larger number by the smaller one. 2. If x or y is zero, stop. The answer is the nonzero value. 3 If neither x nor y is zero, go back to step 1. Here is an example listing the successive values of x and y: XIII O 135 15 15 0 y 20 20 5 5 } (135/ 20) = 15 (20 / 15) = 5 (15 / 5) = 0 GCD = 5 Write a recursive method that finds the GCD of two numbers using Euclid's algorithm. public class Arithmetic { public static int gcd (int a, int b) { // Your work here Lab 15.2 Tester for GCD Write a tester program for your GCD algorithm.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Need the tester and main program done in Java.
Transcribed Image Text:Lab 15.1 Greatest Common Divisor
A formula for finding the greatest common divisor (GCD) of two numbers was formulated by the
mathematician Euclid around 300 BCE. The GCD of two numbers is the largest number that will divide
into both numbers without any remainder. For example, the GCD of 12 and 16 is 4, the GCD of 18 and
12 is 6.
The basic algorithm is as follows:
Assume we are computing the GCD of two integers x and y. Follow the steps below:
1. Replace the larger of x and y with the remainder after (integer) dividing the larger number by the
smaller one.
2. If x or y is zero, stop. The answer is the nonzero value.
3 If neither x nor y is zero, go back to step 1.
Here is an example listing the successive values of x and y:
y
20
20
5
5
135
15
15
0
NN
(135/ 20) = 15
(2015) = 5
(15/5) = 0
}
GCD = 5
Write a recursive method that finds the GCD of two numbers using Euclid's algorithm.
public class Arithmetic
{
public static int gcd (int a, int b)
{
// Your work here
Lab 15.2 Tester for GCD
Write a tester program for your GCD algorithm.
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