Factors of a Natural Number in C++

Factors of n in C++: every i from 1 to n where n % i == 0. 24 → 1 2 3 4 6 8 12 24.

BeginnerLoop ProgramsExample 13 of 14

factors-of-a-natural-number.cpp

1#include <iostream>
2using namespace std;
3
4int main() {
5    int num;
6    
7    cout << "Enter a number: ";
8    cin >> num;
9    
10    cout << "Factors of " << num << " are: ";
11    
12    for (int i = 1; i <= num; i++) {
13        if (num % i == 0) {
14            cout << i << " ";
15        }
16    }
17    cout << endl;
18    
19    return 0;
20}

Output

Enter a number: 24
Factors of 24 are: 1 2 3 4 6 8 12 24

What's going on

A factor of n divides n with remainder 0. Factors of 24: 1 2 3 4 6 8 12 24.

cin >> num;

Sample 24.

for (int i = 1; i <= num; i++)

if (num % i == 0) cout << i << " ";

Walk 24: 1 yes, 2 yes, 3 yes, 4 yes, 5 no, 6 yes, … 24 yes.

Prime 7 prints 1 7. 1 prints 1. 0 is a mess (every i divides 0); this loop would run zero times or behave badly depending on i <= 0. Don't type 0.

You can stop at sqrt(num) and print i and num/i as a pair. This program checks every i through n. Fine for 24. Slow for 10^9.

Order is increasing because i goes 1, 2, 3, ….

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