The nth Catalan number in terms of binomial coefficients is calculated by the formula(n + k )/k where k varies from 2 to n and n ≥ 0. i.e.Cn = (2n)!/((n+1)!n!)Programpublic class NthCatalanNumber {    public static long fact(int i) {       if(i

The nth Catalan number in terms of binomial coefficients is calculated by the formula(n + k )/k where k varies from 2 to n and n ≥ 0. i.e.Cn = (2n)!/((n+1)!n!)Programpublic class CatalanNumbers {    public static long fact(int i) {       if(i

Following is the Java program which prints the kth prime factor of a number n, when k and n are given.Programimport java.util.Scanner; public class KthPrimeFactor {    public static void main(String args[]) {       int number, k, factor = 0;       Scanner sc = new Scanner(System.in);       System.out.println("Enter a number :");             number = sc.nextInt();       System.out.println("Enter the k value :");       k = sc.nextInt();       int temp = k-1;             for(int i = 2; i< number; ... Read More

The numbers which can be expressed as the sum of positive consecutive integers are known as polite numbers.Ex: 5 = 2+3The number of ways a number can be expressed as the sum of positive integers will be the Politeness of that number.Ex: 9 = 4+5 || 2+3+4AlgorithmGet the prime factors of a number.Get the powers of prime factors greater than 2.Add 1 to all of them.Multiply them, subtract 1 from the result.Programimport java.util.Scanner; public class PolitenessOfANumber {    public static void main(String args[]) {       Scanner sc = new Scanner(System.in);       System.out.println("Enter a number");   ... Read More

Following is the Java program which prints all the sum of all the divisors of a given number.

Following is the Java program which prints all the divisors of a given number.Programimport java.util.Scanner; public class DivisorsOfNaturalNumber {    public static void main(String args[]) {       Scanner sc = new Scanner(System.in);       System.out.println("Enter required number :");       int num = sc.nextInt();             for(int i = 1; i

If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.Some examples of numbers divisible by 3 are as follows.The number 85203 is divisible by 3 because the sum of its digits (8 + 5 + 2 + 0 + 3 = 18) is divisible by 3.The number 79154 is not divisible by 3 because the sum of its digits (7 + 9 + 1 + 5 + 4 = 26) is not divisible by 3.Programimport java.util.Scanner; public class DivisibleBy3 {    public static void main(String args[]) {       Scanner sc = new Scanner(System.in);       System.out.println("Enter a number :");       String num = sc.nextLine();       int digitSum = 0;             for(int i = 0; i

A number is divisible by 11 if the difference between the sum of its alternative digits is divisible by 11.i.e. if (sum of odd digits) – ( sum of even digits) is 0 or divisible by 11 then the given number is divisible by 11.Programimport java.util.Scanner; public class DivisibleBy11 {    public static void main(String args[]) {       Scanner sc = new Scanner(System.in);       System.out.println("Enter a number :");       String num = sc.nextLine();       int digitSumEve = 0;       int digitSumOdd = 0;            for(int i = 0; i

If the sum of the digits of a number is divisible by 9, then the number is divisible by 9.Some examples of numbers divisible by 9 are as follows. The number 51984 is divisible by 9 because the sum of its digits (5+ 1 + 9 + 8 + 4 = 27) is divisible by 9.The number 91403 is not divisible by 9 because the sum of its digits (9 + 1 + 4 + 0 + 3 = 17) is not divisible by 9.Programimport java.util.Scanner; public class DivisibleBy9 {    public static void main(String args[]) {       Scanner sc = new Scanner(System.in);       System.out.println("Enter a number :");       String num = sc.nextLine();       int digitSum = 0;       for(int i = 0; i

ProgramFollowing is the example to calculate the GCD of the numbers of an array.Live Demopublic class GCDOfArrayofNumbers{    public static int gcd(int a,int b){       int res = 0;       while (b > 0){          int temp = b;          b = a % b;          a = temp;          res = a;       }       return res;    }    public static void main(String arg[]){       int[] myArray = {3, 6, 8};       int result = gcd(myArray[0],myArray[1]);       for(int i = 2; i < myArray.length; i++){          result = gcd(result, myArray[i]);       }       System.out.println("Gcd of n numbers is: "+result);    } }OutputGCD of n numbers is: 1