Perfect number

A number is called perfect if the number is equal to the sum of its divisors (the number itself is not considered a divisor in this case).

Check Perfect Number

#include <iostream>
using namespace std;

int main() {
    int number, sum = 0;

    cout << "Enter a number to check for perfect: ";
    cin >> number;

    for (int i = 1; i < number; i++) {
        if (number % i == 0) {
            sum = sum + i;
        }
    }

    if (sum == number) {
        cout << number << " is a perfect number";
    }
    else {
        cout << number << " is not a perfect number";
    }

    return 0;
}

Output

Enter a number to check for perfect: 28
28 is a perfect number

Code Explanation

The first two lines include the iostream library and the std namespace, which provides access to the standard input and output streams (cin and cout) used in the code.

void checkPerfect(int max) {
    int number, min = 1, i, sum = 0;

This is the definition of the function checkPerfect. It takes an integer argument max, which represents the upper bound for finding perfect numbers. Inside the function, several variables are declared:

• number: the number being tested to see if it’s a perfect number
• min: the lower bound for finding perfect numbers, initialized to 1
• i: a loop counter used in the inner loop to test the divisors of number
• sum: the sum of the divisors of number, initialized to 0

    for (number = min; number <= max; number++) {
        sum = 0;
        for (i = 1; i < number; i++) {
            if (number % i == 0) {
                sum = sum + i;
            }
        }

The first for loop iterates over the numbers from min to max. Inside the loop, sum is reset to 0, and another for loop is used to test the divisors of number. The inner loop uses the modulo operator (%) to check if i is a divisor of number, and if so, adds i to sum.

        if (sum == number) {
            cout << number << " is a perfect number" << endl;
        }

If the sum of the divisors of number is equal to number itself, then number is considered a perfect number, and is output to the screen.

    }
}

The end of the checkPerfect function.

int main() {
    int max;

    cout << "Enter the upper bound to find perfect numbers: ";
    cin >> max;

    checkPerfect(max);

    return 0;
}

The main function is the entry point of the program. It first prompts the user to enter the upper bound for finding perfect numbers, then calls the checkPerfect function with the user’s input as an argument. The return 0; statement indicates that the program has executed successfully.

Perfect Number List (1-n)

#include <iostream>
using namespace std;

void checkPerfect(int max) {
    int number, min = 1, i, sum = 0;

    for (number = min; number <= max; number++) {
        sum = 0;
        for (i = 1; i < number; i++) {
            if (number % i == 0) {
                sum = sum + i;
            }
        }
        if (sum == number) {
            cout << number << " is a perfect number" << endl;
        }
    }
}

int main() {
    int max;

    cout << "Enter the upper bound to find perfect numbers: ";
    cin >> max;

    checkPerfect(max);

    return 0;
}

Output

Enter the upper bound to find perfect numbers: 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Code Explanation

void checkPerfect(int max) {
    int number, min = 1, i, sum = 0;

This is the definition of the function checkPerfect. It takes an integer argument max, which represents the upper bound for finding perfect numbers. Inside the function, several variables are declared:

• number: the number being tested to see if it’s a perfect number
• min: the lower bound for finding perfect numbers, initialized to 1
• i: a loop counter used in the inner loop to test the divisors of number
• sum: the sum of the divisors of number, initialized to 0

    for (number = min; number <= max; number++) {
        sum = 0;
        for (i = 1; i < number; i++) {
            if (number % i == 0) {
                sum = sum + i;
            }
        }

The first for loop iterates over the numbers from min to max. Inside the loop, sum is reset to 0, and another for loop is used to test the divisors of number. The inner loop uses the modulo operator (%) to check if i is a divisor of number, and if so, adds i to sum.

        if (sum == number) {
            cout << number << " is a perfect number" << endl;
        }

If the sum of the divisors of number is equal to number itself, then number is considered a perfect number, and is output to the screen.

    }
}

The end of the checkPerfect function.

int main() {
    int max;

    cout << "Enter the upper bound to find perfect numbers: ";
    cin >> max;

    checkPerfect(max);

    return 0;
}

The main function is the entry point of the program. It first prompts the user to enter the upper bound for finding perfect numbers, then calls the checkPerfect function with the user’s input as an argument. The return 0; statement indicates that the program has executed successfully.