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- # Exercise 1. Implement the algorithm covered in lectures that determines if an integer n is prime. Your function should return True, if n is prime, and False otherwise. Your algorithm has to be effective for n ~ 1,000,000,000,000.def isPrime(n):The greatest common divisor of two positive integers, A and B, is the largest number that can be evenly divided into both of them. Euclid’s algorithm can be used to find the greatest common divisor (GCD) of two positive integers. You can use this algorithm in the following manner: Compute the remainder of dividing the larger number by the smaller number. Replace the larger number with the smaller number and the smaller number with the remainder. Repeat this process until the smaller number is zero. The larger number at this point is the GCD of A and B. Write a program that lets the user enter two integers and then prints each step in the process of using the Euclidean algorithm to find their GCD. An example of the program input and output is shown below: Enter the smaller number: 5 Enter the larger number: 15 The greatest common divisor is 5use JAVA to write the code. : Euclid’s algorithm for finding the greatest common divisor (gdc) of two numbers The algorithm: given two numbers, n1 and n2: Divide n1 by n2 and let r be the remainder. If the remainder r is 0, the algorithm is finished and the answer is n2. (If the remainder is 1, the numbers are mutually prime and we are done-see below.) Set n1 to the value of n2, set n2 to the value of r, and go back to step 1. Entering 0 for one of the values is bad. It should work for the other value, but you have to figure out which is OK and which is bad. Catch this problem as it happens and make the user enter another value until they enter an acceptable one. Give an appropriate error message if this happens.
- Write an algorithm that reads 10 integer numbers and calculates the average for numbers that are divisible by 5.Q3 :Write an algorithm to find the multiplication of odd numbers from a list of size 10 integer numbers ? E RA A - 1E- Times NWe want to print the character “*” as the following pattern. For example, for n = 5, we have a 5*5 .
- Find the numbers that can be expressed as the product of two nonnegative integers insuccession and print them in increasing order. (For example, 30 is such a number as it can bewritten as the product of 5 and 6 (30=5x6), which are two numbers in succession.) The user shouldspecify a maximum value and the program should print all said numbers smaller than or equal tothat value. The program should keep a count of how many numbers were printed and should output that count ,as well as the numbersFind the numbers that can be expressed as the product of two nonnegative integers insuccession and print them in increasing order. (For example, 30 is such a number as it can bewritten as the product of 5 and 6 (30=5x6), which are two numbers in succession.) The user shouldspecify a maximum value and the program should print all said numbers smaller than or equal tothat value. The program should keep a count of how many numbers were printed and shouldoutput that count, as well as the numbers. creat a git bash script for the problem aboveCorrect answer will be upvoted else downvoted. number is called 2050-number if it is 2050, 20500, ..., (2050⋅10k for integer k≥0). Given a number n, you are asked to represent n as the sum of some (not necessarily distinct) 2050-numbers. Compute the minimum number of 2050-numbers required for that. Input The first line contains a single integer T (1≤T≤1000) denoting the number of test cases. The only line of each test case contains a single integer n (1≤n≤1018) denoting the number to be represented. Output For each test case, output the minimum number of 2050-numbers in one line. If n cannot be represented as the sum of 2050-numbers, output −1 instead.
- le.com/forms/d/e/1FAlpQLSc6PlhZGOLJ4LOHo5cCGEf9HDChfQ-tT1bES-BKgkKu44eEnw/formResponse The following iterative sequence is defined for the set of positive integers: Sn/2 3n +1 ifn is odd if n is even Un = Using the rule above and starting with 13, we generate the following sequence: 13 u13 = 40 u40 =20 u20 = 10→ u10 =5 u5 = 16 u16 = 8 ug = 4 → Us =2 u2 =1. It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. The below function takes as input an integer n and returns the number of terms generated by the sequence starting at n. function i-Seq (n) u=n; i=%3; while u =1 if statement 1 u=u/2; else statement 2 end i=i+1; end statement 1 and statement 2 should be replaced by: None of the choices statement 1 is "mod(u,2)=D%3D0" and statement 2 is "u = 3*u+1;" statement 1 is "u%2" and statement 2 is "u = 3*u+1;" O statement 1 is "mod(n,2)=30" and statement 2 is "u = 3*n+1;"* Euclid's algorithm (or the Euclidean algorithm) is an algorithm that computes the greatest common divisor, denoted by gcd, of two integers. Below are the original version of Euclid's algorithm that uses repeated subtraction and another one that uses the remainder. int gcd sub (a,b) int gcd rem(a,b) int a,b; int a,b; { { if (!a) int t; return b; while (b) while (b) { if (a > b) = b; a = a - b; b = a % b; else a t; b = b - a; } return a; return a; } } 1. Trace each of the above algorithm using these values: a=24 and b = 18. Show your work 2. Compare both algorithms. That is, which one is better and why? Show your work.Let A = {a, b, c} and B = {u, v}. Write a. A × B b. B × A
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