Find the GCD of 72 and 100 using the Euclidean GCD algorithm.
In Java
The answer to this question is as follows:
The code is as follows:
import java.util.*;
public class GCD
{
public static int gcd_numbers(int value1, int
value2)
{
if (value1 == 0)
return
value2;
return gcd_numbers(value2%value1,
value1);
}
public static void main(String[] args)
{
int value1 = 72, value2= 100;
System.out.println("GCD of
"+value1+" and "+value2+" is:"+gcd_numbers(value1, value2));
}
}
The input and ouput is as follows:
Find the GCD of 72 and 100 using the Euclidean GCD algorithm. In Java
a Find the greatest common divisor (gcd) of 322 and 196 by using the Euclidean Algorithm. gcd- By working back in the Euclidean Algorithm, express the gcd in the form 322m196n where m and n are integers b) c) Decide which of the following equations have integer solutions. (i) 322z +196y 42 ii) 322z +196y-57
Write a java program that implements euclidean algorithm to calculate gcd of any two numbers.
Using the Euclidean Algorithm show that gcd (193, 977) Now find integers s, t such that 193s +977t-1, and use this to find the value of a that satisfies the congruence 193a 38 (mod 977) Using the Euclidean Algorithm show that gcd (193, 977) Now find integers s, t such that 193s +977t-1, and use this to find the value of a that satisfies the congruence 193a 38 (mod 977)
6. Using the Euclidean Algorithm show that gcd (109, 736) 1 Now find integers s, t such that 109s + 736t 1, and use this to find the value of r that satisfies the congruence 109x 71 (mod 736). 6. Using the Euclidean Algorithm show that gcd (109, 736) 1 Now find integers s, t such that 109s + 736t 1, and use this to find the value of r that satisfies the congruence 109x 71 (mod 736).
1. (15 points) Use the Euclidean Algorithm to find GCD(344,72). Note: You must show all major steps of the algorithm to derive your answer.
PROBLEM 1 For each of the following pairs of integers, use the Euclidean Algorithm to find ged(a,b), and to write gcd(a,b) as a linear combination of a and b, i.e. find integers m and n such that gcd(a,b) = am + bn. (a) a = 36, b = 60. (b) a = 12628, b = 21361. (c) a = 901, b = -935. (d) a = 72, b = 714. (e) a = -36, b = -60.
2,3,4,5,6 please 2. Use the Euclidean algorithm to find the following: a gcd(100, 101) b. ged(2482, 7633) 3. Prove that if a = bq+r, then ged(a, b) = ged(b,r). such that sa tb ged(a,b) for the following pairs 4. Use Bézout's theorem to find 8 and a. 33, 44 b. 101, 203 c. 10001, 13422 5. Prove by induction that if p is prime and plaja... An, then pla, for at least one Q. (Hint: use n = 2 as...
(i.e. running the Euclidean algorithm backwards), find the general solution to each of the following: We were unable to transcribe this image250382 36972Y gcd (25038, 36972) 3219x + 6351y- gcd (3219,6351)
can somebody help me with this exercise 5 Euclidean algorithm The largest common divisor (gcd) of two positive integers p and q can be given by the Euclid's algorithm explained in the lecture will be determined. · Write a function gcdIterative that uses the largest common divisor of p and q Calculates loop structure and returns. Use the pseudocode given in the lecture as a starting point and implement it as directly as possible into a C ++ program. Use...
Question 1. (a) Find the greatest common divisor of 10098 and 3597 using the Euclidean Algorithm. (b) Find integers a and a2 with 1009801 +3597a2 = gcd(10098,3597). (c) Are there integers bı and b2 with 10098b1 + 3597b2 = 71? Justify your answer. (d) Are there integers ci and c2 with 10098c1 + 3597c2 = 99? Justify your answer. Question 2. Consider the following congruence. C: 21.- 34 = 15 (mod 521) (a) Find all solutions x € Z to...