C++ program to find numbers with K odd divisors in a given range

In this problem, we are given three integer values, L, R, and k. Our task is to find numbers with K divisors in a given range. We will be finding the count of numbers in the range [L, R] that have exactly k divisors. We will be counting the 1 and the number itself as a divisor.

Let’s take an example to understand the problem,


a = 3, b = 10, k = 4




Numbers with exactly 3 divisors within the range 3 to 10 are
6 : divisors = 1, 2, 3, 6 8 : divisors = 1, 2, 4, 8

Solution Approach

A simple solution to the problem is by counting the k divisors.. So, we will count the number of divisors for all numbers in the range. And if the count of divisors in k, we will add 1 to the number count.

Program to illustrate the working of our solution,


 Live Demo

using namespace std;
int countDivisors(int n) {
   int divisors = 0;
   for (int i=1; i<=sqrt(n)+1; i++) {
      if (n%i==0) {
         if (n/i != i)
            divisors ++;
   return divisors;
int countNumberKDivisors(int a,int b,int k) {
   int numberCount = 0;
   for (int i=a; i<=b; i++) {
      if (countDivisors(i) == k)
   return numberCount;
int main() {
   int a = 3, b = 10, k = 4;
   cout<<"The count of numbers with "<<k<<" divisors is "<<countNumberKDivisors(a, b, k);
   return 0;


The count of numbers with 4 divisors is 2

Updated on: 16-Mar-2021


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