C Program to Find All Factors of Number

In this article, we will learn to write a C program to print all distinct divisors of a number n. Factors of a number are the positive integers that divide the number without leaving a remainder. For example, for n = 10, the factors will be 1, 2, 5 and 10.

Note: This problem is different from finding all prime factors.

A Simple Solution to find all the factors of a number is to iterate all the numbers from 1 to n check if the current number divides n and print the current number.

C Program to Display Factors of a Number

C

// C implementation of Naive
// method to print all divisors
#include <stdio.h>

// Function to print the divisors
void printDivisors(int n)
{
    for (int i = 1; i <= n; i++)
        if (n % i == 0)
            printf("%d ", i);
}

// Driver code
int main()
{
    printf("The divisors of 100 are: ");
    printDivisors(100);

    return 0;
}

Output

The divisors of 100 are: 1 2 4 5 10 20 25 50 100 

Complexity Analysis

• Time Complexity: O(n)
• Auxiliary Space: O(1)

We can optimize this time complexity to O(sqrt(n)) by observing that all the divisors are present in pairs. For example if n = 100, then the pairs of divisors are: (1,100), (2,50), (4,25), (5,20), (10,10). Refer to the article Find all factors of a Natural Number for O(sqrt(n)) solution.

But this solution will not print the factors in the sorted order. Please refer to the article Find all divisors of a natural number | Set 2 for an O(sqrt(n)) solution that prints divisors in sorted order.