Why is this considered "Medium" difficulty?

#include <iostream>
#include <stdexcept>

using namespace std;

int largest_proper_divisor(int n) {
        if (n == 0) {
                throw invalid_argument("largest proper divisor is not defined for n=0");
        }
        if (n == 1) {
                throw invalid_argument("largest proper divisor is not defined for n=1");
        }
        for (int i = n/2; i >= 1; --i) {
                if (n % i == 0) {
                        return i;
                }
        }
        return -1; // will never happen
}

void process_input(int n) {
        try
        {
                if(n==0 || n==1)
                        throw invalid_argument("largest proper divisor is not defined for n=");
                else{
                         int d = largest_proper_divisor(n);
                        cout << "result=" << d << endl;
                } 


        }
        catch(const std::invalid_argument& e)
        {
                cout<<e.what()<<n<<endl;
        }
        cout << "returning control flow to caller";

}


int main() {
        int n;
        cin >> n;
        process_input(n);
        return 0;
}

Easy money.

#include <iostream>
#include <stdexcept>

using namespace std;

int largest_proper_divisor(int n) {
    if (n == 0) {
        throw invalid_argument("largest proper divisor is not defined for n=0");
    }
    if (n == 1) {
        throw invalid_argument("largest proper divisor is not defined for n=1");
    }
    for (int i = n/2; i >= 1; --i) {
        if (n % i == 0) {
            return i;
        }
    }
    return -1; // will never happen
}

void process_input(int& n) {
    try {
        int d = largest_proper_divisor(n);
        cout << "result=" << d << endl;
    } catch (const std::invalid_argument& e) {
        cout << e.what() << endl;
    }
    cout << "returning control flow to caller" << endl;
}


int main() {
    int n;
    cin >> n;
    process_input(n);
    return 0;
}

invalid _argument is a class derived from logic error then exception class... so you can write that instead:

 catch (const exception& e){
        cout<<e.what()<<endl;
    }