Write a c++ program to find all numbersless than 1000 which are:
1) divisible by 7?
2) divisible by 11?
3) divisible by 7 but not divisible by 11?
4) divisible by both 7 and 11?
5) notdivisible by 7 or 11? .

The c++ program is shown below.

#include <iostream>

using namespace std;

int main() {    

   cout<<"Numbers less than 1000 which are divisible by 7"<<endl;    

   for(int k=1; k<1000; k++)

   {

       // number should give remainder 0 which show complete divisibility

       if(k%7 == 0)

           cout<<k<<"\t";

   }    

   cout<<endl<<"Numbers less than 1000 which are divisible by 11"<<endl;    

   for(int k=1; k<1000; k++)

   {

       if(k%11 == 0)

           cout<<k<<"\t";

   }    

   cout<<endl<<"Numbers less than 1000 which are divisible by 7 but not divisible by 11"<<endl;    

   for(int k=1; k<1000; k++)

   {

       // for 11, number should not give remainder 0 which shows incomplete divisibility

       if(k%7 == 0 && k%11 != 0)

           cout<<k<<"\t";

   }    

   cout<<endl<<"Numbers less than 1000 which are divisible by 7 and divisible by 11"<<endl;

   for(int k=1; k<1000; k++)

   {

       if(k%7 == 0 && k%11 == 0)

           cout<<k<<"\t";

   }    

   cout<<endl<<"Numbers less than 1000 which are not divisible by 7 and not divisible by 11"<<endl;    

   for(int k=1; k<1000; k++)

   {

       if(k%7 != 0 && k%11 != 0)

           cout<<k<<"\t";

   }    

   return 0;

}

Explanation:

The test for divisibility is done by using the modulus operator which is used as a condition inside the if statement. This test is done inside for loop.

All the numbers from 1 to 999, less than 1000, are divided by 7 and/ or 11 depending on the sub question. Only the numbers which are completely divisible are displayed. Divisible numbers give remainder 0 always.

The divisibility test by 7 is shown below.

cout<<"Numbers less than 1000 divisible by 7"<<endl;    

   for(int k=1; k<1000; k++)

   {

       if(k%7 == 0)

           cout<<k<<"\t";

   }    

In other words, all the numbers divisible by 7 are same as the numbers in the table of 7.

The same logic shown above is applied for other sub questions to test for divisibility by 11 and combination of 7 and 11.

To improve readability, tabs and new lines are inserted at appropriate places.