Unable to assign string variable to vectors via PUSH_BACK from a .dat file inside a loop?

I am required to read contents of a file and then modify it and then store it on vectors for easy manipulation. But unfortunately, Push_back cannot assign a string variable. I have looked for another solution online, nothing matches mine.

 #include <iostream>
    #include <fstream>
    #include <string>
    #include <algorithm>
    #include <vector>
    using namespace std;
  int main () {
      // Initializing variables and vectors
      size_t pos;
      string last_name;
      string first_name;
      string number{};
      string full_name{};
      string line{};
      ifstream myfile ("employees.dat");
      vector<string > number_vector;
      vector<string> last_name_vector;
      vector<string> first_name_vector;

      // Reading File Contents:
      if (myfile.is_open())
      {
        while ( myfile.good() )
        {
          getline (myfile,line);

           // Extracting Numbers from Lines
            for (size_t i {0}; i < line.length(); ++i){
             if (line[i] == '#'){
                 line.clear();
             }

             else if (isdigit (line[i]))
                 number += line[i]; 
             // Extracting Full Name

             else if (isalpha(line[i])  || line[i] == ' ') 
                 full_name += line[i];


         }

          number_vector.push_back(full_name);
         cout<< (number_vector[0]); 

        }              

        myfile.close();
      }
             else cout << "Unable to open file"<<endl; 

      return 0;
    }